Teleseismic recordings (Δ>87¿) of a deep earthquake beneath the Banda Sea at stations in Tanzania show a difference in the arrival time of the radial (SSV) and transverse component (SSH)S wave ranging from 1--3 s. Shear velocity anisotropy in the lowermost mantle beneath the Indian Ocean is the likely cause of this signal because recordings at the same stations of closer-in events (Δ<80¿) in the same source region do not present a comparable differential travel time. For the Banda Sea event, the SSH signals are broader than SSV signals, suggesting that a discontinuity (or strong vertical gradient) in primarily VSH marks the sudden onset of transverse isotropy in D″ (with a magnitude of 1.4--2.7%) about 350 km above the coremantle boundary. SKKS coda, S-to-p converted phases at the Moho, and upper mantle heterogeneity beneath the stations obscure the onset of SSV and complicate wave shapes. It is therefore difficult to evaluate whether general anisotropy needs to be invoked into a model of shear velocity anisotropy. ¿ 2000 American Geophysical Union