Abstract: By a general result of Kechris-Solecki-Todorcevic the Borel chromatic number of 2^{Z^n} is no more than 2n+1. While this upper bound is achievable on the free part of 2^{Z^n}, we consider the problem of computing the Borel chromatic number for the free part of 2^{Z^n}. The theorem is that it is either 3 or 4 (exactly which is unknown). This is joint work with Steve Jackson and Ben Miller.