What do language models (LMs) do with language? Everyone agrees that they produce sequences of (mostly) coherent sentences. But are they saying anything with those strings or simply babbling in a convincing simulacrum of language use? This is a vague question, and there are many ways of making it precise. Here we will address one aspect of the question, namely, whether LMs' words refer: that is, whether the outputs of LMs achieve "word-to-world" connections. There is prima facie reason to think they do not since LMs do not interact with the world in the way that ordinary language users do. Drawing on insights from the externalist tradition in philosophy of language, we argue that appearances are misleading and that there is good reason to think that LMs can refer.