In this talk, we present a simple and efficient method for rotating a spherical harmonic expansion. This is a well-studied problem, arising in classical scattering theory, quantum mechanics and numerical analysis, usually addressed through the explicit construction of the Wigner rotation matrices. Existing fast algorithms, based on recurrence relations, are subject to a variety of instabilities, limiting the effectiveness of the approach for expansions of high degree. We show that rotation can be carried out easily and stably through "pseudospectral" projection, without ever constructing the matrix entries themselves. In the simplest version of the method, projection is carried out on the equator of the rotated sphere. If only the lowest angular modes are required, the algorithm can be further accelerated by using a sequence of constant latitude circles. This is joint work with Leslie Greengard.