We examine the utility of a curriculum (a means of presenting training samples in a meaningful order) in unsupervised learning of probabilistic grammars. We introduce the {\em incremental construction hypothesis} that explains the benefits of a curriculum in learning grammars and offers some useful insights into the design of curricula as well as learning algorithms. We present results of experiments with (a) carefully crafted synthetic data that provide support for our hypothesis and (b) natural language corpus that demonstrate the utility of curricula in unsupervised learning of probabilistic grammars.