We study the homology of [Pn,Pn], the commutator subgroup of the pure braid group on n strands, and show that Hl([Pn,Pn]) contains a free abelian group of infinite rank for all 1≤l≤n−2. As a consequence we determine the cohomological dimension of [Pn,Pn]: for n≥2 we have cd([Pn,Pn])=n−2.