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It is a renowned Chabad custom to avoid eating all processed foods on Pesach, as much as possible.
Matzah and wine: The above custom is with exception to Matzah and wine, which due to inability to self produce, is widely purchased from a store or company. Nevertheless, many families are stringent to produce their own wines and even bake their own Matzahs.
Oil: The Rebbe writes that “Anash use Natala margarine on Pesach”. This refers to a congealed cottonseed oil that was processed by a company under a local Mehadrin Hashgacha. Thus, one may purchase any Kosher for Pesach oil that contains a most reliable Hashgacha. Nevertheless, there are those who are stringent to only use melted chicken fat [Shmaltz] as their oil base product for Pesach food and cooking.
Dairy: The Rebbe ate dairy products on Pesach.
Chocolate: There is no source for the statement that the Rebbe ate chocolate on Pesach. He would however, eat sugarless chocolate during the year.
Sugar: See C!
From what time are those who are accustomed to not eat processed foods to begin their stringency? From the night of Pesach or from 5th hour of Erev Pesach?
One who is stringent to avoid eating processed foods is to avoid doing so starting from the 5th hour of Erev Pesach. However, many are lenient to eat processed foods up until the night of Pesach.
One may not eat salt and other spices on Pesach unless it has a reliable Hashgacha, as we suspect that perhaps Chametz becomes mixed into the salt.
The custom of the Rebbe Rashab: The Rebbe Rashab avoided using sugar due to suspicion that a Chametz ingredient was used in the boiling process, or alternatively the workers would dip their breads into it, and there is thus a suspicion that a crumb of Chametz remained in the sugar. There is a story with the brother-in-law of the Rebbe Rashab who owned a sugar production plant and had made a specially supervised batch of sugar to be used by the Rebbe Rashab on Pesach, despite that even throughout the year there was no suspicion of Chametz in the sugar. When the Rebbe Rashab was brought the sugar cubical his face became stern with concern, and he followed to break open one of the cubicles, and unexplainably a wheat kernel fell out.
The Rebbe’s directive: Regarding if the above stringency of the Rebbe Rashab applies for all Chassidim, the Rebbe once said that if one knows for certain that there is no suspicion of Chametz in the sugar then he does not see a reason for one to be stringent.
The custom to boil the sugar: Some are accustomed to boil sugar before Pesach and thus make sugar water which they use rather than actual sugar. Some have the custom to then filter the sugar water afterwards.
Fish is to be purchased with a proper Hashgacha for Pesach, as often those who market them place starch and other products that may be problematic.
The Chabad custom, as well as the custom of many others, is not to drink alcohol on Pesach [other than wine], even if it has a Hashgacha for Pesach.
Garlic is not Chametz, or Kitniyos, and is thus permitted to be eaten over Pesach. Nevertheless, there are those who are accustomed not to eat garlic on Pesach. Those families who are accustomed to follow this custom are not to swerve from it. However, those families who did not receive such a custom are not required to accept it upon themselves. Nevertheless, if one is part of a community in which everyone is accustomed to be stringent, he is not to be lenient in public regarding this matter.
The Chabad custom: Some record that there is no Chabad custom to avoid eating garlic on Pesach. [Practically, each family is to follow their Minhag.]
Cinnamon is not Chametz, or Kitniyos, and is thus permitted to be used over Pesach. Nevertheless, some are accustomed not to eat cinnamon on Pesach, and so is the Chabad custom. because it may contain Chametz.
Fresh ginger: One may eat fresh ginger that has no worry of Chametz.
Horseradish should only be purchased with a Hashgacha, who verifies that non-Chametz knives are used to cut it.
Not to eat hot foods on Pesach:
Some have the custom not to eat hot foods [of 110 degrees] on Pesach being that their teeth cannot be properly Kashered.
Food that fell on the ground:
Food which fell on the ground is not eaten on Pesach, although if the food has a peel there are those who peel it, and then use the food.
 The source of the custom: This custom is not recorded in the Poskim, or compilations of Chabad Pesach customs, but is the widely accepted Minhag.
 The reason: Seemingly, this custom is based on the custom of the Alter Rebbe not to eat at other people’s houses on Pesach due to that we are not aware of their level of stringency. [See Halacha 11] Thus, we avoid eating processed foods being that it is equivalent to foods made in other people’s homes. [Nitei Gavriel 40 p. 218] Alternatively, the reason behind this custom is because we suspect that perhaps in the production line, which involves hundreds of people of various backgrounds, Chametz fell into the food and has not disintegrated. [This can easily occur if a worker had a sandwich and did not wash his hands properly afterwards. Having worked as a Mashgiach in a Kosher for Pesach food production, I can attest that it is almost impossible to ascertain that all the workers wash their hands from all Chametz leftovers prior to beginning work on the line.] According to this reason, one is to avoid processed foods beginning from the time of prohibition to eat Chametz from the 5th hour of Erev Pesach, as Chametz Beiyn which is found in a food is at times not nullified even before the night of Pesach. [See Admur 442 Kuntrus Acharon 15; 466:9-11; Shut Rabbeinu 18; See Piskeiy Admur Yoreh Deah chapter 100; Shach 109:8; “A Semicha Aid for learning the Laws of Taaruvos” Chapter 104:4] Alternatively, perhaps we suspect for even disintegrated Chametz, as we suspect for the opinion in 447:22 who holds that we say Chozer Veniur by all foods that contain Chametz of any amount, even taste, even if it was nullified before Pesach. According to this reason one is only to be stringent in avoiding eating processed foods beginning form the night of Pesach.
 Igros Kodesh Vol. 21 p. 96. This was a written telegram to Anash of some part of America or Canada in 1949.
 Heard from the Rebbe’s secretary, Rav Binyamin Klein and Rav Leibel Groner; Some say this was likewise the custom of the Rebbe Rayatz and Rebbe Rashab
 Response of Rabbi Yehuda Leib Groner [secretary of the Rebbe] to a query of the author; Custom of many of Anash from vintage Chabad homes as heard by the author
The reason: The reason for not eating processed foods is due to a suspicion of Taaruvos Chametz. Now, before the night arrives, although Chametz can be nullified, this only applies if it is a mixture of Yaveish Beyaveish or Lach Belach. However, by a mixture of Yaveish Belach it is not nullified even before Pesach. [Admur 442 Kuntrus Acharon 15; 466:9-11; Shut Rabbeinu 18; See Piskeiy Admur Yoreh Deah chapter 100; “A Semicha Aid for learning the Laws of Taaruvos” Chapter 104:4] Thus, if there is a crumb of Chametz that fell into the processed food and is still intact it is not nullified and one transgresses eating Chametz on Pesach.
 Custom of many families of Anash.
The reason: Seemingly the reason behind the leniency on Erev Pesach until the night, despite that which is explained above, is because on the night of Pesach begin the severe stringencies of Issur Mashehu, and Issur Kareis for eating Chametz. Thus, although from a Halachic perspective there can be suspicion of Chametz in processed foods even before the night of Pesach in a way that it is not nullified, nevertheless one only begins to suspect for this starting from the night. Vetzaruch Iyun. Alternatively, perhaps it is because we suspect for the opinion in 447:22 who holds that starting from the night of Pesach we say Chozer Veniur by all foods that contain Chametz of any amount, even taste, even if it was nullified before Pesach.
 Admur 462:19
 See Sefer Hasichos 5700 p. 37; Otzer Minhagei Chabad Nissan p. 50; Shulchan Menachem 2:267
 Hamelech Bemisibo 1:307; See Shulchan Menachem ibid
 Chayeh Adam 127:3 in name of Noda Beyehuda
 The reason: This is done in order to ascertain, that even if there were to be a speck of Chametz in the sugar, it would dissolve through the cooking and become nullified in 60x before Pesach in Lach Belach. [ibid]
 Madrich of Eida Hachareidis
 Otzer Minhagei Chabad Nissan p. 61; See Admur 447:36 and gloss of Maharil
 The reason: This is due to suspicion that the salt contained Chametz. Although from the letter of the law, it may be eaten, as even if there is Chametz the fish can be washed off before Pesach from any possible salt. A student of the Tzemach Tzedek discovered that besides for the above suspicion there is a Chametz ingredient added to the gravy and therefore it’s forbidden on Pesach according to the letter of the law. [See Otzer Minhagei Chabad ibid]
 Sources in Otzer Minhagei Chabad Nissan p. 54 based on Tzemach Tzedek and Rav Akiva Eiger; See Admur 451:44; Tzemach Tzedek 51;
 The Tzemach Tzedek would not drink any alcohol/liquor on Pesach even if it was supposedly made without Chametz, and so was the custom also of the Rebbe Rashab. Rebbe Akivah Eger sent a proclamation prohibiting it without a revealed reason, saying that he is saving the reason for himself. This proclamation is mentioned in the Teshuvahs of the Tzemach Tzedek and seems to be the source for why the Tzemach Tzedek avoided drinking it. In many places this stringency became widespread while in others it did not. Amongst Rabbanei Anash, there were those who ruled that it may be drunk on Pesach.
 Otzer Minhagei Chabad Nissan p. 62; The Rebbe Rashab said that the Tzemach Tzedek forbade radishes on Pesach without giving any explanation. The Rebbe Rashab himself would sell his radish jelly before Pesach.
 Chayeh Adam 127:7; See Nitei Gavriel 2-39:7
 See Sdei Chemed Asifas Diunim Chametz Umatzah 6 Mareches Ayin; Nitei Gavriel 39:5; Otzer Minhagei Chabad p. 63
 Chayeh Adam 127:7; Daas Torah 467:2; Zecher Yehosef 120; Madanei Shulchan 117:25; See Beis Yosef 460; Nitei Gavriel ibid
 P”M 464 A”A 1 “Some are accustomed not to eat garlic on Pesach”; Chemdas Moshe 22; Pischa Zuta 2:7 that so was custom of Belz [Minhagei Belz p. 41]; Meishiv Halacha 1:309; Otzer Minhagei Chabad Nissan p. 63; Shevach Hamoadim p. 195
The reason: The Poskim state that they do not know the reason behind this custom. [P”M ibid; Rav of Belz stated Otzer ibid] Some however suggest that the reason is because in the times of the Temple people would avoid garlic due to its bad odor which may prevent them from making the pilgrimage to the Temple, as rules Rambam Chagiga 2:2. [Dover Meisharim p. 111]
 Rav of Belz ibid “Al Titosh Toras Imecha”; However see P”M ibid that one is not to be lenient in this matter in front of an ignoramus although he may be lenient in private in front of Torah scholars.
 Bitzel Hachachma 4:113; However see P”M ibid that one is not to be lenient in this matter in front of an ignoramus although he may be lenient in private in front of Torah scholars.
 See P”M ibid
 Hiskashrus 922 in name of Rav Yaakov Landau; Rav Eli Landau wrote to me in a correspondence that while his father did use garlic during Pesach in Eretz Yisrael, in Russia they did not eat it.
 See Sdei Chemed Asifas Diunim Chametz Umatzah 6 Mareches Ches; Nitei Gavriel 39:6; Otzer Minhagei Chabad p. 63
 Lev Ledavid, brought in Sdei Chemed ibid; Maadanei Shmuel 117:34; See Yad Ahron 16:138
 See Sdei Chemed ibid; Orchos Chaim 467 in name of Meorei Or
 Sefer Haminhagim p. 76
 See Nitei Gavriel 2-39:4
 Admur 455:33 and 473:33 and 481:1
 Haggadah of Rebbe; Sefer Haminhagim p. 39; Otzer Minhagei Chabad 36; It is referred there as Keida.
 Rav Eli Landau in email correspondence; Rabbi Groner responded that whether one may eat fresh ginger is to be given to the ruling of a Rav and is not negated by Chabad custom.
 See Madrich of Eida Hachareidis
 See Piskeiy Teshuvos 451:23
 Otzer Minhagei Chabad Nissan p. 60