There are few things as beautiful as natural materials such as stone and wood, and I am always amazed at how eager some people are to cover them over with paint. Often people just like the fresh look of a new coat of paint, but I contend that beauty is a lot more than just a fresh look!
Some antiques *look* old and shabby to the untrained eye, and it is often not until the owner has been advised of its value that he begins to see the piece in a new light. A stone fireplace can be like that, too (especially if it's been carefully cleaned, and not *all tarnished with ashes and soot*).
Another reason some will choose to paint over natural beauty is to make it *fit in* with a room's decor. I would contend that a room's biggest asset (which a fireplace often is) should be the starting point of it's decorative plans, not merely an afterthought.
Of course, you may have already considered these things, but thanks for letting me say my piece.
p.s. My wife recently had me stop the car so she could chide the owner of a neighborhood store who was painting over the store's natural stone facade. While I wouldn't have gone that far, I certainly agreed with how she felt!
p.p.s. In order to get good adhesion from a coat of paint, the fireplace has to be well cleaned, anyway. Why don't you do that first, then decide if you really want to paint ...