Children face an enormously difficult task in learning their native language. It is widely believed that they do not receive or make little use of negative evidence (Marcus, 1993), and yet it has been proven that many classes of languages less powerful than natural languages cannot be learned in the absence of negative evidence (Gold, 1964). In this paper we present an approach to learning good approximations to members of one such class of languages, the regular languages, based on positive evidence alone.