It's not a show stopper for a regional, or a major anymore for that matter. Just know that there are more obstacles in your way than there are for most.
For starters when you go to get your first class medical the FAA will want in writing your drinking habits, past and present, and possibly a substance abuse evaluation.
Also make sure you disclose this to them, and all employers. The airlines do an FBI fingerprint check and federally the only thing that doesn't show up is an expunged record, PBJ, Deferred Adjudication, all that only really helps at the state level and with private companies not regulated by a federal entity. So be ready to explain it and what you've learned from it. If you really want to make it to a major look for other opportunities to make your resume stand out because you will have to overcome that blemish.