  Computer simulations of sheared granular fluids, modeled as inelastic hard
spheres, are presented which show signs of a uniquely three-dimensional
instabilty. In the stable regime, a linear velocity profile, $v_{x}=ay$, with
shear rate $a$ is established using Lees-Edwards boundary conditions. In the
unstable regime, the velocity profile aquires a dependence on the third
dimension of the form $v_{x}=ay+sin(2\pi z/L)$ in a cubic box with sides of
length $L$. An analysis of the linearized Navier-Stokes equations shows the
presence of an instability and gives a simple expression for the critical
wavevector which is quantitatively consistent with the results of simulations
and which indicates that the instability persists at low densities.
