Vacuum nodes in QCD at theta=pi: Exact results

We show that the vacuum functional of 3 + 1 dimensional non abelian gauge theories vanishes for some classical field configurations psi(0)(A) = 0 when the coefficient of the CP violating theta term becomes theta = pi (mod. 2 pi). Some of these classical configurations are explicitly identified and include sphalerons. The results shed new light Into the nonperturbative behavior of nonabelian gauge theories and suggest a relevant role for these classical configurations in the confinement mechanism at theta = 0.