Many large-scale scientific computations require eigenvalue solvers in a scaling regime where efficiency is limited by data movement. We introduce a parallel algorithm for computing the eigenvalues of a dense symmetric matrix, which performs asymptotically less communication than previously known approaches. We provide analysis in the Bulk Synchronous Parallel (BSP) model with additional consideration for communication between a local memory and cache. Given sufficient memory to store c copies of the symmetric matrix, our algorithm requires Θ( √c) less interprocessor communication than previously known algorithms, for any c ≤ p1/3 when using p processors. The algorithm first reduces the dense symmetric matrix to a banded matrix with the same eigenvalues. Subsequently, the algorithm employs successive reduction to O(log p) thinner banded matrices.We employ two newparallel algorithms that achieve lower communication costs for the full-to-band and band-to-band reductions. Both of these algorithms leverage a novel QR factorization algorithm for rectangular matrices.