We give a new randomized algorithm for achieving consensus among asynchronous processes that communicate by reading and writing shared registers. The fastest previously known algorithm, due to Abrahamson, has expected running time 2°^\ Our algorithm is polynomial, requiring an expected 0 ( n 4 ) operations. Applications of this algorithm include the elimination of critical sections from concurrent data structures and the construction of asymptotically unbiased shared coins. This research was partially sponsored by the Office of Naval Research (DOD), under Contract N00014-88-K-0641. The work of J. Aspnes was supported by a National Science Foundation Graduate Fellowship. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency, the National Science Foundation or the U.S. government.