We used long-period surface waves from teleseismic earthquakes recorded by the TERRAscope network to determine phase velocity dispersion of Rayleigh waves up to periods of about 170 sec and of Love waves up to about 150 sec. This enabled us to investigate the upper-mantle velocity structure beneath southern California to a depth of about 250 km. Ten and five earthquakes were used for Rayleigh and Love waves, respectively. The observed surface-wave dispersion shows a clear Love/Rayleigh-wave discrepancy that cannot be accounted for by a simple isotropic velocity model with smooth variations of velocity with depth. Separate isotropic inversions for Love- and Rayleigh-wave data yield velocity models that show up to 10% anisotropy (transverse isotropy). However, tests with synthetic Love waves suggest that the relatively high Love-wave phase velocity could be at least partly due to interference of higher-mode Love waves with the fundamental mode. Even after this interference effect is removed, about 4% anisotropy remains in the top 250 km of the mantle. This anisotropy could be due to intrinsic anisotropy of olivine crystals or due to a laminated structure with alternating high- and low-velocity layers. Other possibilities include the following: upper-mantle heterogeneity in southern California (such as the Transverse Range anomaly) may affect Love- and Rayleigh-wave velocities differently so that it yields the apparent anisotropy; higher-mode Love-wave interference has a stronger effect than suggested by our numerical experiments using model 1066A. If the high Love-wave velocity is due to causes other than anisotropy, the Rayleigh-wave velocity model would represent the southern California upper-mantle velocity structure. The shear velocity in the upper mantle (Moho to 250 km) of this structure is, on average, 3 to 4% slower than that of the TNA model determined for western North America.