  Let k be a field, and let {\pi}:\tilde{X} -> X be a proper birational
morphism of irreducible k-varieties, where \tilde{X} is smooth and X has at
worst quotient singularities. When the characteristic of k is zero, a theorem
of Koll\'ar in [Ko1] says that {\pi} induces an isomorphism of etale
fundamental groups. We give a proof of this result which works for all
characteristics. As an application, we prove that for a smooth projective
irreducible surface X over an algebraically closed field k, the etale
fundamental group of the Hilbert scheme of n points of X, where n > 1, is
canonically isomorphic to the abelianization of the etale fundamental group of
X. Koll\'ar has pointed out how the proof of the first result can be extended
to cover the case of quotients by finite group schemes.
