Artificial intelligence (AI) is a rapidly developing general purpose technology of global importance. This paper examines the potential competition issues arising from the physical infrastructure underpinning AI development, particularly computing resources such as advanced chips. It explores the structure of AI supply chains, identifies key players and highlights characteristics that make these markets susceptible to competition issues. The paper also considers the tools available to competition authorities and assesses their relevance and limitations in addressing emerging challenges. Finally, it discusses how effective competition in AI infrastructure markets relies on competition authorities closely monitoring market developments and responding with a balanced mix of enforcement and advocacy tools.