Conventional crystalline magnets are characterized by symmetry breaking and normal modes of excitation called magnons with quantized angular momentum . Neutron scattering correspondingly features extra magnetic Bragg diffraction at low temperatures and dispersive inelastic scattering associated with single magnon creation and annihilation. Exceptions are anticipated in socalled quantum spin liquids as exemplified by the one-dimensional spin-1/2 chain which has no magnetic order and where magnons accordingly fractionalize into spinons with angular momentum /2. This is spectacularly revealed by a continuum of inelastic neutron scattering associated with two-spinon processes and the absence of magnetic Bragg diffraction. Here, we report evidence for these same key features of a quantum spin liquid in the three-dimensional Heisenberg antiferromagnet NaCaNi 2 F 7 . Through specific heat and neutron scattering measurements, Monte Carlo simulations, and analytic approximations to the equal time correlations, we show that NaCaNi 2 F 7 is an almost ideal realization of the spin-1 antiferromagnetic Heisenberg model on a pyrochlore lattice with weak connectivity and frustrated interactions. Magnetic Bragg diffraction is absent and 90% of the spectral weight forms a continuum of magnetic scattering not dissimilar to that of the spin-1/2 chain but with low energy pinch points indicating NaCaNi 2 F 7 is in a Coulomb phase. The residual entropy and diffuse elastic scattering points to an exotic state of matter driven by frustration, quantum fluctuations and weak exchange disorder.