I have taken paint off of brick many times. I use any non-toxic chemical peeler. It's actually pretty easy to get paint off of brick. However, since it is a fireplace I would have to say to make certain the chemical is both non-toxic and non-flamable. I would also call the manufacturer to ask about its application in a brick fireplace.
Cheers, Christopher A. Kinkade, Griffith, IN USA
"The difference between a cook and a chef is understanding what's going on." - Alton Brown