We introduce a novel approach named unam-biguity regularization for unsupervised learning of probabilistic natural language grammars. The approach is based on the observation that natural language is remarkably unambiguous in the sense that only a tiny portion of the large number of possible parses of a natural language sentence are syntactically valid. We incorporate an inductive bias into grammar learning in favor of grammars that lead to unambiguous parses on natural language sentences. The resulting family of algorithms includes the expectation-maximization algorithm (EM) and its variant, Viterbi EM, as well as a so-called softmax-EM algorithm. The softmax-EM algorithm can be implemented with a simple and computationally efficient extension to standard EM. In our experiments of unsupervised dependency grammar learning, we show that unambiguity regularization is beneficial to learning, and in combination with annealing (of the regularization strength) and sparsity priors it leads to improvement over the current state of the art.