  Let X be a quasiprojective smooth surface defined over an algebraically
closed field of positive characteristic. We show that if X is Frobenius split
then so is the Hilbert scheme Hilb^n(X) of n points in X. In particular, we get
the higher cohomology vanishing for ample line bundles on Hilb^n(X) when X is
projective and Frobenius split.
