In Data Oriented Parsing (DOP), an annotated language corpus is used as a virtual stochastic grammar. An input string is parsed by combining subtrees from the corpus. As a consequence, one parse tree can usually be generated by several derivations that involve different subtrees. This leads to a statistics where the probability of a parse is equal to the sum of the probabilities of all its derivations. In (Scha, 1990) an informal introduction to DOP is given, while (Bod, 1992) provides a formalization of the theory. In this paper we show that the maximum probability parse can be estimated in polynomial time by applying Monte Carlo techniques. The model was tested on a set of hand-parsed strings from the Air Travel Information System (ATIS) corpus. Preliminary experiments yield 96% test set parsing accuracy.