Found this guy on our live rock a few weeks ago, but I suspect it has been there all along and is just now visible.
What is it? It does not move around the rock, and its halves will pinch closed periodically. Is it a sponge of some type?
It is not uncommon to have hitch hiker bivalves like clams or mussels and I suspect that is what it is. A bit tough to tell from the picture but your description points to that.