The goal of constraint acquisition is to learn exactly a constraint network given access to an oracle that answers truthfully certain types of queries. In this paper we focus on partial membership queries and initiate a systematic investigation of the learning complexity of constraint languages. First, we use the notion of chain length to show that a wide class of languages can be learned with as few as O(n log(n)) queries. Then, we combine this result with generic lower bounds to derive a dichotomy in the learning complexity of binary languages. Finally, we identify a class of ternary languages that eludes our framework and hints at new research directions.