A novel nonlocal supercurrent, carried by quartets, each consisting of four electrons, is expected to appear in a voltage-biased three-terminal Josephson junction. This supercurrent results from a nonlocal Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the dc Josephson current, exists only in equilibrium, the ABS, which gives rise to the quartet supercurrent, persists in the nonlinear regime. In this work, we report such resonance in a highly coherent three-terminal Josephson junction made in an InAs nanowire in proximity to an aluminum superconductor. In addition to nonlocal conductance measurements, cross-correlation measurements of current fluctuations provided a distinctive signature of the quartet supercurrent. Multiple device geometries had been tested, allowing us to rule out competing mechanisms and to establish the underlying microscopic origin of this coherent nondissipative current.