We present the results of a Monte Carlo study of the surfaces (or hulls) of percolation clusters in three dimensions. The hulls were generated using a novel growing self-avoiding surface. Our results strongly suggest that the surface and bulk of the infinite cluster have the same fractal dimension at the percolation threshold, and that the other bulk and hull critical exponents are identical as well. These conclusions are supported by heuristic scaling arguments. © 1991 The American Physical Society.