The clause chain is an under-investigated complex sentence type, found in hundreds of languages. In a clause chain, as many as 20 or more ‘medial’ clauses with under-specified verbal predicates combine with a single ‘final’ clause with fully-specified verbal predicate. Clause chains are of interest for three main reasons: (a) the special syntactic relationship between clauses, which is neither textbook subordination nor coordination; (b) the potential extreme length of a single chain; and (c) switch-reference marking in clause chains of some languages could require speakers to plan at least one clause ahead as they speak. Research on child production of complex sentences has largely overlooked clause chains. Longitudinal data for three children aged 1;1 to 3;3 acquiring the Papuan language Nungon show that Nungon-speaking children begin producing clause chains around the age of 2;4, with a marked increase in rate of use around age 2;11. Chain length is limited to two clauses until age 3;1. Different-subject marking in medial clauses is used by all three children early, but is first attested in one-clause, ‘root medial’ contexts, rather than in chains. Bayesian statistical models confirm the strong tendency for children to use root medials in expressions of desires and commands. Children’s production of three types of complex sentences—clause chains, subordinated final clauses, and coordinated final clauses—is shown to be subject to the same type of developmental constraint; but once development reaches an adequate level for increased complex sentence production, children acquiring Nungon produce many more clause chains than complex sentences involving subordinated or coordinated final clauses.