In this paper we present a computational study of lexical acquisition. We attempt to characterize the lexical acquisition task faced by children by defining a simplified formal approximation of this task which we term the mapping problem. We then present a novel strategy for solving large instances of this mapping problem. This strategy is capable of learning the word-to-meaning mappings for as many as 10,000 words given corpora of 20,000 utterances. Such lexical acquisition is accomplished in a language independent fashion without any reference to the syntax of the language being learned.