We consider the possibility that the velocity structure of D″ is anisotropic. The data we examined consist of seismograms from 9 deep Japanese earthquakes recorded at WWSSN receiver stations in North America. The source-receiver combinations span distances of 70¿--106¿ with associated S waves passing through D″ beneath Alaska. Differential travel times of the S, Scd, ScS and SKS phases are used to constrain the velocity structure in D″. Shear waves refracted by D″ are observed beyond 72.2¿ and provide a sensitive measurement of the velocity structure in D″. Beyond 93¿, the vertically polarized (SV) and horizontally polarized (SH) shear waves often appear distinctly split, although, at distances less than 89¿ the components are more nearly synchronous. Near 94¿, SH occurs as a double arrival. SV in this range, however, remains a single arrival roughly synchronous with the second SH arrival. We have been unable to reproduce these effects in isotropic model synthetics. Synthetics for transversely isotropic models have been computed that do match these waveforms. The anisotropy was constrained to be only within D″, with a vertical symmetry axis. We conclude that these observations may be explained by an anisotropic D″ layer. The D″ discontinuity may be due to a transition to anisotropic mantle a few hundred kilometers above the core-mantle boundary. ¿ American Geophysical Union 1996