  Anderson localization (AL) is a ubiquitous interference phenomenon in which
waves fail to propagate in a disordered medium. We observe three-dimensional AL
of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi
gas to expand into a disordered potential. A two-component density distribution
emerges consisting of an expanding mobile component and a nondiffusing
localized component. We extract a mobility edge that increases with the
disorder strength, whereas the thermally averaged localization length is shown
to decrease with disorder strength and increase with particle energy. These
measurements provide a benchmark for more sophisticated theories of AL.
