Does chocolate furniture, navy blue fireplace tile, and purple accent pillows go together in a living room?

purple and chocolate would / should work quite well but the navy blue might not be such a visual delight with these other colours - however, not much you can do about the tiles unless you paint or replace them - you could add a few more navy accents to maike the whole theme flow better - but that said, it is surprising what can work if you accessorise right