I had the exact situation on my brick/ornamental stone fireplace. To answer your question, yes, there is a way to safely remove the paint. I used a product called Peel Away 7. This is paint stripper which comes in a paste and you brush it on and then cover it with the Peel Away paper. After waiting (can be up to 24hrs), you pull away the paper and the paint comes off. The last step is to neutralize the stripped area and rinse with water. Overall, the product performed quite nicely but here are a few things to consider:
1) Depending on how many layers of paint you have, you must apply the peel away thick enough to work. Be sure to get inside the mortar joints of the brick.
2) Be patient! The longer the stuff sits, the more easily the paint comes off.
3) Remember to cover the entire paste area with the Peel Away paper (otherwise it dries out and you're back to square one.)
4) Cut the Peel Away Paper to size FIRST! When you're done applying the paste you can put the paper on right away. I can't stress the importance of this! The stuff can dry pretty fast if the temperature is warm.
5) Don't the let product's clain fool you. This still will be a bear of a job and all the paint may not come off in ONE application. I found that when I pulled the paper off, I still had to scrape. Overall, the fumes are not that bad.
6) Because the Peel away is quite expensive, consider using the old fashioned liquid stripper (which contains methyl chloride). It is a lot cheaper and works almost as well if you can tolerate the fumes. However, it is a heck of a lot more corrosive on your skin so cover up. Also, the clean-up with a liquid stripper is a lot messier. In either case, move all furniture, caprets, etc. out of the way and tape the areas you to protect. If you do decide to go with the Peel Away, DO NOT buy the neutralizer. It is just vinegar they sell for $20 a gallon. Regular household vinegar (5%) works just as well.
I hope you find my experiences useful. The end result is a beautiful fireplace that you will be proud of. Let me know how things work out.