Practitioners frequently take multiple samples from large language models (LLMs) to explore the distribution of completions induced by a given prompt. While individual samples can give high-quality results for given tasks, collectively there are no guarantees of the distribution over these samples induced by the generating LLM. In this paper, we empirically evaluate LLMs’ capabilities as distributionsamplers. We identify core concepts and metrics underlying LLM-based sampling, including different sampling methodologies and prompting strategies. Using a set of controlled domains we evaluate the error and variance of the distributions induced by the LLM. We find that LLMs struggle to induce reasonable distributions over generated elements, suggesting that practitioners should more carefully consider the semantics and methodologies of sampling from LLMs.