Using the Very Long Baseline Array and the European Very Long Baseline Interferometry Network, we have made a precise measurement of the radio parallax of the black hole X-ray binary MAXI J1820+070, providing a model-independent distance to the source. Our parallax measurement of (0.348+/-0.033) mas for MAXI J1820+070 translates to a distance of (2.96+/-0.33)kpc. This distance implies that the source reached (15+/-3) per cent of the Eddington luminosity at the peak of its outburst. Further, we use this distance to refine previous estimates of the jet inclination angle, jet velocity, and the mass of the black hole in MAXI J1820+070 to be (63+/-3){deg}, (0.89+/-0.09)c, and (9.2+/-1.3)M_{sun}_, respectively