ChatGPT is a popular information system (over 1 billion visits in August 2023) that can generate natural language responses to user queries. It is important to study the quality and equity of its responses on health-related topics, such as vaccination, as they may influence public health decision-making. We use the Vaccine Hesitancy Scale (VHS) proposed by Shapiro et al. to measure the hesitancy of ChatGPT responses in English, Spanish, and French. We find that: (a) ChatGPT responses indicate less hesitancy than those reported for human respondents in past literature; (b) ChatGPT responses vary significantly across languages, with English responses being the most hesitant on average and Spanish being the least; (c) ChatGPT responses are largely consistent across different model parameters but show some variations across the scale factors (vaccine competency, risk). Results have implications for researchers interested in evaluating and improving the quality and equity of health-related web information.