Anomalous double-pulse teleseismic P-wave arrivals were observed at one station near the northern margin of the Tibetan Plateau. The azimuthal dependence of the waveform distortion and its absence at nearby stations indicated that the distortion was produced by receiver-side crustal heterogeneity. Modeling of the three-component data revealed a 15- to 20-kilometer Moho offset that occurs over a narrow Lateral range of Less than 5 kilometers. This east-west-striking offset separates the thick Tibetan Plateau crust from the Qaidam Basin crust. Such a sharp crustal thickness change implies a weak Tibetan Plateau crust that thickens vertically in response to penetration by India from the south and to blockage caused by a strong Qaidam Basin crust to the north.