. 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.The full control over all quantum mechanical degrees of freedom of a chemical reaction allows the identification of fundamental interaction processes and the steering of chemical reactions. This task is often complicated in heteronuclear systems by a multitude of possible reaction channels, which make theoretical treatments very challenging. Therefore, focussing on the best-controlled experimental conditions, such as using state-selected single particles and low temperatures, is crucial for the investigation of chemical processes at the most elementary level. The hybrid system of trapped atoms and ions offers key advantages in this undertaking. On the one hand, ion traps offer a large potential well depth to trap the reaction products for precision manipulation and investigation. On the other hand, contrary to pure ionic systems, there is no Coulomb barrier between the particles to fundamentally prevent chemical reactions at low temperatures. Therefore, the efforts to control the motional degrees of freedom of one 4-6 and both 7-13 reactants in hybrid atom-ion systems have paved new ways towards cold chemistry. The yet missing component is the simultaneous control of the internal degrees of freedom.The interaction between an ion and a neutral atom at long distances is dominated by the attractive polarization interaction potential V (r), which is of the formHere, C 4 = α 0 q 2 /(4π 0 ) 2 is proportional to the neutral particle polarizability α 0 , q is the charge of the ion, 0 is the vacuum permittivity, and r is the internuclear separation. Inelastic collisions take place at short internuclear distances. In the cold, semiclassical regime this requires collision energies above the centrifugal barrier [14][15][16] . Such processes are referred to as Langevin-type collisions and happen, even for cold collisions 7,9 , at an energyindependent rate γ Langevin = 2π √ C 4 /µ n a . Here µ is the reduced mass of the collision partners and n a is the neutral atom density.Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK. *e-mail: cs540@cam.ac.uk. More subtle effects, such as the hyperfine interaction, which may lead to atom-ion Feshbach resonances, are not included in the polarization potential and have been investigated only theoretically so far 17 . Experimentally, reactive Langevin collisions in the polarization potential have been investigated in ground state collisi...