Abstract:``Theory of Mind" (ToM) is the ability to understand human thinking and decision-making, an ability that plays a crucial role in many types of social interaction between people, including linguistic communication. This paper investigates to what extent recent Large Language Models in the ChatGPT tradition possess ToM. Focussing on six well-known ToM problems, we posed each problem to two versions of ChatGPT and compared the results under a range of prompting strategies. While the results concerning ChatGPT-3 were somewhat inconclusive, ChatGPT-4 was shown to arrive at the correct answers more often than would be expected based on chance, although correct answers were often arrived at on the basis of false assumptions or invalid reasoning.