There are a few chess playing sites which accept bitcoins and allow PvP matches. They have already been mentioned before, just read the thread from the beginning and you will not ask questions that have already been asked and most likely answered here. It is not very long and makes an interesting read by itself.
Though I still doubt anyone will be able to earn anything there.
Do you have the name of a few because i checked google and didn't find much.
I'm not quite sure about the first site, I mean whether it accepts bitcoins (didn't investigate into this issue), but the second one seems to be accepting as well as paying prizes in bitcoins.
I'd like to clarify this post, then. lichess.org is the site that the tournaments are hosted on, and the funds are provided by BitChess (where you may also find all the relevant information). So these sites are not separate, really. I think it's ending this week though: I only saw tournaments listings go up until this week, so if you're able to play quickly, it's the time to do so!
They were running back in April of this year IIRC.