The emergence of Artificial Intelligence (AI) tools such as ChatGPT provides an opportunity for software developers to optimize their existing Software Development (SD) processes. We conducted a systematic literature review of 26 articles to understand the current state of literature on the use of ChatGPT to support the productivity of software developers. Three core research themes were identified and elaborated on namely the various applications of ChatGPT, human-AI collaboration, and the impact of ChatGPT on productivity. The findings which include the emerging applications (e.g. code generation) and impact (e.g. reduced human errors) of ChatGPT, are relevant to organizations that intend to leverage AI to effectively support the SD processes as well as software developers who intend to leverage ChatGPT to support their productivity during the SD process. Areas of future research are also proposed given the gaps identified in literature