Gravitationally bound three-body systems have been studied for hundreds of years1, 2 and are common in our Galaxy3, 4. They show complex orbital interactions, which can constrain the compositions, masses and interior structures of the bodies5 and test theories of gravity6, if sufficiently precise measurements are available. A triple system containing a radio pulsar could provide such measurements, but the only previously known such system, PSR B1620-26 (refs 7, 8; with a millisecond pulsar, a white dwarf, and a planetary-mass object in an orbit of several decades), shows only weak interactions. Here we report precision timing and multiwavelength observations of PSR J0337+1715, a millisecond pulsar in a hierarchical triple system with two other stars. Strong gravitational interactions are apparent and provide the masses of the pulsar (1.4378(13)
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