Media coverage suggests that ChatGPT can pass examinations based on multiple choice questions (MCQs), including those used to qualify doctors, lawyers, scientists etc. This poses a potential risk to the integrity of those examinations. We reviewed current research evidence regarding the performance of ChatGPT on MCQ-based examinations in higher education, along with recommendations for how educators might address challenges and benefits arising from these data. 53 studies were included, covering 114 question sets, totalling 49014 MCQs. Free versions of ChatGPT based upon GPT-3/3.5 performed better than random guessing but failed most examinations, performing significantly worse than the average human student. GPT-4 passed most examinations with a performance that was on a par with human subjects. These findings indicate that all summative MCQ-based assessments should be conducted under secure conditions with restricted access to ChatGPT and similar tools, particularly those examinations which assess foundational knowledge.