:
It is better to find a different Baal Koreh if there is one. However, if he will be very insulted then you can let him read for the Tzibbur, Bdiavad.
Explanation:
The Mishna in in Megillah (19b) states: Everyone is allowed to read the Megillah, except for a Cheresh-Deaf person, Shoteh-a crazy person, and a Katan-child.
The Gemara explains that the Cheresh the Mishna is talking about is one can’t hear (even if he can talk is completely lucid) since we rule like R’ Yossi (Berachot ch.2 Mishna 3) that If one reads Shema but can’t hear himself, he fulfilled his mitzvah, R’ Yossi says he didn’t.” That R’ Yossi rules that in order to fulfil a mitzvah of Kriah one must hear himself. Therefore, a deaf person can’t read the megillah, since he can’t hear himself. Since we are not stringent like R’ Yossi by Kriat Shema then by Kriat HaMegilla we should be lenient.
However, Maran Beit Yosef 689 asks why does the Rambam rule by Hilchot Kriat Shema not like R’ Yossi that he doesn’t have to hear himself. In Hilchot Megillah (1:2), on the other hand, he rules if a Cheresh reads the Megillah the one who hears him does not fulfill this mitzvah?
The Beit Yosef answers that Kriat Megillah is more stringent than Shema because of Pirsumei Nisa, we need publicize the miracle.
The Mishna Berura adds that the Ta”z who explains that one fulfils his mitzvah only where he can hear just he didn’t say it loud enough, but if he can’t hear at all he does not have the heter of the Rabanan.
Therefore, someone who can’t hear can’t read for the tzibbur.
What is Halacha of one who can hear, but only with a hearing aid?
The Shaarei Teshuva bring a case of someone who can hear if you shout loudly into his ear. Then he can read for other people. Therefore, if the Baal Koreh can hear a little if someone shouts loudly without the hearing aid, then he can read the megillah even with the hearing aid, because it is like shouting. However, if he can’t hear at all without the hearing aid then is better to find someone else to read the megillah. However, since a hearing aid only works for someone who can hear a little bit then the chazan probably can hear a little and if he will be insulted, you should let him read it. (Cochlear implants have a different halacha and are not being discussed here.)
