Is chess recursive?

Chess is a formal system. Here is why:
initial positions<====> axioms
Any configuration on the board is easily checked if it is a valid arrengement, so, there is formation rules.
Any configuration derivable from the initial position <===> theorems

But, can it describe itself, or made statements about it self? No, or yes?

Godel uses godel numbering to map theorem in a formal system to numeral relations. Can this be done with chess? Could the godel number for such confirguration be a proof of that configuration?