Many complex generative systems use languages to create structured objects. We consider a model of random languages, defined by weighted context-free grammars. As the distribution of grammar weights broadens, a transition is found from a random phase, in which sentences are indistinguishable from noise, to an organized phase in which nontrivial information is carried. This marks the emergence of deep structure in the language, and can be understood by a competition between energy and entropy.

Note: no background in linguistics will be assumed.