Yes you can paint marble but a shame to do so, firstly you should give it a good clean with a solvent as it probably has years of wax based polish built up on it, then undercoat it and gloss or put whatever on it, but beware that oils in paint is liable to permanently stain the marble, so you may not have the option of returning it to its former glory.
if you don't like amrble, remove the fireplace and sell it. could be worth a bob or 2. then put in whatever you want. As Ratter15 ays it's a pity to ruin the marble
(some people would die for a marble fireplace)