Non-human animal chimeras, containing human neurological cells, have been created in the laboratory. Despite a great deal of debate, the status of such beings has not been resolved. Under normal definitions, such a being could either be unconventionally human or abnormally animal. Practical investigations in animal sentience, artificial intelligence, and now chimera research, suggest that such beings may be assumed to have no legal rights, so philosophy could provide a different answer. In this vein, therefore, we can ask: What would a chimera, if it could think, think about? Thinking is used to capture the phenomena of a novel, chimeric being perceiving its terrible predicament as no more than a laboratory experiment. The creation of a thinking chimera therefore forces us to reconsider our assumptions about what makes human beings (potentially) unique (and other sentient animals different), because, as such, a chimera’s existence bridges our social and legal expectations about definitions of human and animal. Society has often evolved new social norms based on different kinds of (ir)rational contrivances; the imperative of non-contradiction, which is defended here, therefore requires a specific philosophical response to the rights of a thinking chimeric being.