Improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms1, and coherent light–matter interfaces have been built2, 3. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms4 and to search for variations of fundamental constants in precision atomic clocks5. Until now, atomic quantum gases and single trapped ions have been treated separately in experiments. Here we investigate whether they can be advantageously combined into one hybrid system, by exploring the immersion of a single trapped ion into a Bose–Einstein condensate of neutral atoms. We demonstrate independent control over the two components of the hybrid system, study the fundamental interaction processes and observe sympathetic cooling of the single ion by the condensate. Our experiment calls for further research into the possibility of using this technique for the continuous cooling of quantum computers6. We also anticipate that it will lead to explorations of entanglement in hybrid quantum systems and to fundamental studies of the decoherence of a single, locally controlled impurity particle coupled to a quantum environment7, 8.