  We prove a long-term regularity result for three-dimensional gravity water
waves with small initial data but nonzero initial vorticity. We consider
solutions whose vorticity vanishes on the free boundary and use this to derive
a system for the evolution of the free boundary which reduces to the
Zakharov/Craig-Sulem formulation in the irrotational case. We are able to
continue the solution until a time determined by the size of the initial
vorticity in such a way that if the vorticity is zero, one recovers a lifespan
$T\sim \epsilon^{-N}$ where $N$ can be taken arbitrarily large if the initial
data is taken to be arbitrarily smooth.
