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Understanding lower-crustal deformational processes and the related features that can be imaged by seismic waves is an important goal in active tectonics. We demonstrate that teleseismic receiver functions calculated for broadband seismic stations in Southern California reveal a signature of pervasive seismic anisotropy in the lower crust. The large amplitudes and small move-out of the diagnostic converted phases, as well as the broad similarity of data patterns from widely separated stations, support an origin primarily from a basal crustal layer of hexagonal anisotropy with a dipping symmetry axis. We conducted neighborhood algorithm searches for depth and thickness of the anisotropic layer and the trend and plunge of the anisotropy symmetry (slow) axis for 38 stations. The searches produced a wide range of results, but a dominant SW-NE trend of the symmetry axis emerged. When the results are divided into crustal blocks and restored to their pre-36 Ma locations, the regional-scale SW-NE trend becomes more consistent, although a small subset of the results can be attributed to NW-SE shearing related to San Andreas transform motion. We interpret this dominant trend as a fossilized fabric within schists, created from top-to-the-SW sense of shear that existed along the length of coastal California during pretransform, early Tertiary subduction or from shear that occurred during subsequent extrusion. Comparison of receiver-function common conversion point stacks to seismic models from the active Los Angeles Regional Seismic Experiment shows a strong correlation in the location of anisotropic layers with "bright" reflectors, further affirming these results.