Large Language Models (LLMs) are often provided as a service via an API, making it challenging for developers to detect changes in their behavior. We present an approach to monitor LLMs for changes by comparing the distributions of linguistic and psycholinguistic features of generated text. Our method uses a statistical test to determine whether the distributions of features from two samples of text are equivalent, allowing developers to identify when an LLM has changed. We demonstrate the effectiveness of our approach using five OpenAI completion models and Meta's Llama 3 70B chat model. Our results show that simple text features coupled with a statistical test can distinguish between language models. We also explore the use of our approach to detect prompt injection attacks. Our work enables frequent LLM change monitoring and avoids computationally expensive benchmark evaluations.