Surface wave dispersion measurements for Love wave overtones carry evidence of azimuthal anisotropy in the transition zone of Earth's mantle (400 to 660 kilometers deep). A Backus-Gilbert inversion of anisotropic phase velocity maps, with resolution kernels mainly sensitive to the transition zone, shows a robust long-wavelength azimuthally anisotropic velocity structure. This observation puts new constraints on the mineralogy and dynamics of the transition zone because this anisotropy may result from aligned minerals, tilted laminated structures, or even organized pockets of fluid inclusions.