Systematic reviews are comprehensive reviews of the literature for a highly focused research question. These reviews are often treated as the highest form of evidence in evidence-based medicine, and are the key strategy to answer research questions in the medical field. To create a high-quality systematic review, complex Boolean queries are often constructed to retrieve studies for the review topic. However, it often takes a long time for systematic review researchers to construct a high quality systematic review Boolean query, and often the resulting queries are far from effective. Poor queries may lead to biased or invalid reviews, because they missed to retrieve key evidence, or to extensive increase in review costs, because they retrieved too many irrelevant studies. Recent advances in Transformer-based generative models have shown great potential to effectively follow instructions from users and generate answers based on the instructions being made. In this paper, we investigate the effectiveness of the latest of such models, ChatGPT, in generating effective Boolean queries for systematic review literature search. Through a number of extensive experiments on standard test collections for the task, we find that ChatGPT is capable of generating queries that lead to high search precision, although trading-off this for recall. Overall, our study demonstrates the potential of ChatGPT in generating effective Boolean queries for systematic review literature search. The ability of ChatGPT to follow complex instructions and generate queries with high precision makes it a valuable tool for researchers conducting systematic reviews, particularly for rapid reviews where time is a constraint and often trading-off higher precision for lower recall is acceptable.