The Olah is initially required to read along together with the Chazan word by word in a low tone, unless he is in the middle of Shema or its blessings, in which case he is not to read along. Nevertheless, it is permitted to give an individual an Aliya even if he is unable to read along with the Baal Korei, such as one who is blind or is illiterate, or is in middle of Shema. He should read it in a low enough tone so that others do not hear, however, he may read it loud enough for his own ears to hear.
 Michaber 141:2-3; Rama 135:4; Tzemach tzedek 35; Sefer Haminhagim p. 13; Shulchan Menachem 1:260
 Rama 139:3 in name of Maharil
 Rama 141:2
Other opinions: Some Poskim rule [Michaber 141:2]