The D " shell at the base of the Earth's mantle is thought to be a thermal and compositional boundary layer where vigorous dynamical processes are taking place(1-4). An important property of D " is its seismic anisotropy, expressed as different velocities for horizontally and vertically polarized shear waves that have been diffracted or reflected at the core-mantle boundary(5,6). The nature of this anisotropy has been the subject of debate(7-11). Here we present an analysis of various seismic phases, generated in the Kermadec-Fiji-Tonga zone and recorded at stations in North America, which reveal a region at the base of the mantle beneath the southwest Pacific Ocean where horizontally propagating vertically polarized waves are slower (by at least 10 per cent) than horizontally polarized waves. This observed anisotropy is an order of magnitude larger than that previously thought to exist in the lower mantle, and corresponds to lateral variations in horizontally polarized shear-wave velocity which are also of about 10 per cent. We speculate that this anisotropy maybe the result of the mixing and shearing of strongly heterogeneous material in the boundary layer.