Coherent quantum transition spectroscopy is a powerful tool in metrology¹, quantum information processing², magnetometry³, and precision tests of the Standard Model⁴. It was applied with great success in proton and deuteron magnetic moment measurements⁵, which culminated in MASER spectroscopy with sub-parts per trillion resolution⁶ and many other experiments at the forefront of physics⁷. All these experiments were performed on macroscopic ensembles of particles, while the coherent spectroscopy of a “free” single nuclear spin has never been reported before. Here, we demonstrate coherent quantum transition spectroscopy of the spin of a single antiproton stored in a cryogenic Penning-trap system. We apply a multi-trap technique⁸, detect the antiproton spin-state using the continuous Stern-Gerlach-effect⁹, and transport the particle to the homogeneous magnetic field of a precision trap (PT). Here, we induce the coherent dynamics and analyze the result by quantum-projection measurements in the analysis trap¹⁰ . We observe for the first time Rabi-oscillations of an antiproton spin and achieve in time-series measurements spin inversion probabilities above 80% at spin coherence times of ≈ 50s. Scans of single-particle spin resonances show inversions >70%, at transition line-widths 16 times narrower than in previous measurements⁸, limited by cyclotron frequency measurement decoherence. This achievement marks a major step towards at least 10-fold improved tests of matter/antimatter symmetry using proton and antiproton magnetic moments.