How do children learn to understand and use complex syntactic constructions? In English, Diessel (2004) shows that they do so in two different ways. Complex sentences with dependent clauses (e.g., "Peter promised that he would come") develop out of simple sentences that are gradually expanded into multi-clause ones. Complex sentences with coordinate clauses (e.g., "He tried hard, but he failed") develop by integrating two independent sentences into a single two-clause unit. Here we expand on that research by focusing on the acquisition of a kind of complex syntactic structure which involves both dependency and coordination—the clause chain—in Ku Waru, a Papuan language spoken in the Western Highlands of Papua New Guinea. Clause chains are constructions coordinating multiple clauses in sequence, where the non-final or "medial" clauses are in a dependent relationship with the final clause. One function of clause chains, which is often taken to be the prototypical one, is to refer to a series of events in sequence. Some Ku Waru clause chains do refer to sequential events. Other Ku Waru clause chains containing particular verbs refer to single events, sometimes with the particular verb providing aspectual or adverbial qualification ("keep doing," "do quickly," etc.). In this article, we track the acquisition of several different kinds of clause chains based on longitudinal recordings of four children acquiring Ku Waru as their first language between the ages of 1½ and 5. We show that, although there are differences among the children in the ages at which they acquire the various kinds of clause chain, all four of them follow the same series of steps in doing so. In conclusion, we compare our findings to Diessel's for English. We find that they are similar in some ways and different in others, which may be related to the differences between subordinate constructions, coordinate non-dependent constructions and coordinate-dependent constructions.