Is it safe to use parchment paper with a baking stone?

I enjoy making bread or pizza on a baking stone, but I don't want to use too much cornmeal to lubricate the transition from pizza peel to the oven. Would using parchment paper be alright, or would it burn on the stone and cause problems with the dough sticking to the stone surface? Would using paper interfere with the crisp crust that a baking stone provides?