  We point out that perturbative evolution in QCD at three loops generates a
strange-antistrange asymmetry s(x)-sbar(x) in the nucleon's sea just from the
fact that the nucleon has non-vanishing up and down quark valence densities.
The recently computed three-loop splitting functions allow for an estimate of
this effect. We find that a fairly sizable asymmetry may be generated. Results
for analogous asymmetries in the heavy-quark sector are also presented.
