Nature Physics – Traditionally, chemical reactions have been investigated by tuning thermodynamic parameters, such as temperature or pressure. More recently, laser or magnetic field control methods have emerged to provide new experimental possibilities, in particular in the realm of cold collisions. The control of reaction pathways is also a critical component to implement molecular quantum information processing. For these studies, single particles provide a clean and well-controlled experimental system. Here, we report on the experimental tuning of the exchange reaction rates of a single trapped ion with ultracold neutral atoms by exerting control over both their quantum states. We observe the influence of the hyperfine interaction on chemical reaction rates and branching ratios, and monitor the kinematics of the reaction products. These investigations advance chemistry with single trapped particles towards achieving quantum-limited control of chemical reactions and indicate limits for buffer-gas cooling of single-ion clocks.