Title: Large language models are not zero-shot communicators. Abstract: The recent success of large language models (LLMs) has drawn heavy attention and investment in their use as conversational and embodied systems. Despite widespread use of LLMs as conversational agents, evaluations of performance fail to capture a crucial aspect of communication: interpreting language in context. Humans interpret language using beliefs, prior knowledge about the world, and more. For example, we intuitively understand the response "I wore gloves" to the question "Did you leave fingerprints?" as meaning "No". To investigate whether LLMs have the ability to make this type of inference, known as an implicature, we design a simple task and evaluate a set of models. We find that despite only evaluating on utterances that require a binary inference (yes or no), most perform close to random. Models adapted to be "aligned with human intent" via reinforcement learning perform much better, but still leave a significant gap with human performance. This gap is even more pronounced for context-heavy utterances. We present our findings as the starting gun for further research into evaluating how LLMs interpret language in context, in order to drive the development of more pragmatic and useful models of human discourse.