A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lglgn) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algorithm uses a novel approach of hashing by \oblivious execution" based on probabilistic analysis to circumvent the parity lower bound barrier at the near-logarithmic time level. The algorithm is simple and is sketched by the following: