We report on experiments in which a spin-polarized current is injected from a GaMnAs ferromagnetic electrode into a GaAs layer through an AlAs barrier. The resulting spin polarization in GaAs is detected by measuring how the tunneling current, to a second GaMnAs ferromagnetic electrode, depends on the orientation of its magnetization. Our results can be accounted for by sequential tunneling with the nonrelaxed spin splitting of the chemical potential, that is, spin accumulation, in GaAs. We discuss the conditions on the hole spin relaxation time in GaAs that are required to obtain the large effects we observe.