We analyze the gravitational binary-lensing event OGLE-2016-BLG-0156, for which the lensing light curve displays pronounced deviations induced by microlens-parallax effects. The light curve exhibits three distinctive widely separated peaks and we find that the multiple-peak feature provides a very tight constraint on the microlens-parallax effect, enabling us to precisely measure the microlens parallax {π }{{E}}. All the peaks are densely and continuously covered from high-cadence survey observations using globally located telescopes and the analysis of the peaks leads to the precise measurement of the angular Einstein radius {θ }{{E}}. From the combination of the measured {π }{{E}} and {θ }{{E}}, we determine the physical parameters of the lens. It is found that the lens is a binary composed of two M dwarfs with masses M 1 = 0.18 ± 0.01 M ☉ and M 2 = 0.16 ± 0.01 M ☉ located at a distance {D}{{L}}=1.35+/- 0.09 {kpc}. According to the estimated lens mass and distance, the flux from the lens comprises an important fraction, ~25%, of the blended flux. The bright nature of the lens combined with the high relative lens-source motion, μ = 6.94 ± 0.50 mas yr-1, suggests that the lens can be directly observed from future high-resolution follow-up observations.