The training and deployment of large language models (LLMs) create a feedback loop with human users: models learn human beliefs from data, reinforce these beliefs with generated content, reabsorb the reinforced beliefs, and feed them back to users again and again. This dynamic resembles an echo chamber. We hypothesize that this feedback loop entrenches the existing values and beliefs of users, leading to a loss of diversity and potentially the lock-in of false beliefs. We formalize this hypothesis and test it empirically with agent-based LLM simulations and real-world GPT usage data. Analysis reveals sudden but sustained drops in diversity after the release of new GPT iterations, consistent with the hypothesized human-AI feedback loop. Code and data available at https://thelockinhypothesis.com