Based on extending the sequential execution model of Prolog to include parallel execution, we present a method for OR-parallel execution of Prolog on a multiprocessor system. The method reduces the overhead incurred by parallel processing. It allows many processing elements (PEs) to process simultaneously a common branch of a search tree, and each of these PEs creates its local environment and selects a subtree for processing without communication. The run-time overhead is small: simple and efficient operations for selecting the proper subtree. Communication is necessary only when some PEs have exhausted their search spaces and there are others still searching for solutions. The method is able to utilize most of the technology devised for sequential implementation of Prolog. It is optimized for an architecture that supports broadcast copying.