We present the first study to investigate Large Language Models (LLMs) in answering radiation oncology physics questions. Because popular exams like AP Physics, LSAT, and GRE have large test-taker populations and ample test preparation resources in circulation, they may not allow for accurately assessing the true potential of LLMs. This paper proposes evaluating LLMs on a highly-specialized topic, radiation oncology physics, which may be more pertinent to scientific and medical communities in addition to being a valuable benchmark of LLMs. We developed an exam consisting of 100 radiation oncology physics questions based on our expertise at Mayo Clinic. Four LLMs, ChatGPT (GPT-3.5), ChatGPT (GPT-4), Bard (LaMDA), and BLOOMZ, were evaluated against medical physicists and non-experts. ChatGPT (GPT-4) outperformed all other LLMs as well as medical physicists, on average. The performance of ChatGPT (GPT-4) was further improved when prompted to explain first, then answer. ChatGPT (GPT-3.5 and GPT-4) showed a high level of consistency in its answer choices across a number of trials, whether correct or incorrect, a characteristic that was not observed in the human test groups. In evaluating ChatGPTs (GPT-4) deductive reasoning ability using a novel approach (substituting the correct answer with "None of the above choices is the correct answer."), ChatGPT (GPT-4) demonstrated surprising accuracy, suggesting the potential presence of an emergent ability. Finally, although ChatGPT (GPT-4) performed well overall, its intrinsic properties did not allow for further improvement when scoring based on a majority vote across trials. In contrast, a team of medical physicists were able to greatly outperform ChatGPT (GPT-4) using a majority vote. This study suggests a great potential for LLMs to work alongside radiation oncology experts as highly knowledgeable assistants.