There is a php chess system available called Online Chess Club (OCC), that i used to play chess with a friend a couple of years back. It isnt your standard chess system though. You simply typed in your move and refreshed the page or logged back in later to see if any move had been made. So im guessing its more suited to distance games.
It was registered members only and from what i could make of it, you could have as many games as you wished running consecutively.
Thinking about it, you could probably get the page to auto refresh by altering the http code and adding a < meta refresh="60" > tag into the head of the template. But you would be generating a fair number of server requests if you did that.
Stats could also be parsed off, and some instructions existed for doing that, but i think its up to the end user to deal with that side of things. I never messed with creating stats as the games were always far from competitive.
Details can be found at.
http://lgames.sourceforge.net/index.php?project=OCC
As for the forum and general server stuff, look at LAMP.