The first fully three-dimensional particle-in-cell (PIC) simulation of whistler turbulence in a magnetized, homogeneous, collisionless plasma has been carried out. An initial relatively isotropic spectrum of long-wavelength whistlers is imposed upon the system, with an initial electron β = 0.10. As in previous two-dimensional simulations of whistler turbulence, the three-dimensional system exhibits a forward cascade to shorter wavelengths and broadband, turbulent spectra with a wave vector anisotropy in the sense of stronger fluctuation energy at k⊥ than at comparable k∥ where the respective subscripts represent directions perpendicular and parallel to the background magnetic field Bo. However, the three-dimensional (3D) simulations display quantitative differences with comparable two-dimensional (2D) computations. In the 3D runs, turbulence develops a stronger anisotropic cascade more rapidly than in 2D runs. Furthermore, reduced magnetic fluctuation spectra in 3D runs are less steep functions of perpendicular wave numbers than those from 2D simulations. The much larger volume of perpendicular wave vector space in 3D appears to facilitate the transfer of fluctuation energy toward perpendicular directions.