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 3 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 $pi_{rm E}$. 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 $theta_{rm E}$. From the combination of the measured $pi_{rm E}$ and $theta_{rm E}$, we determine the physical parameters of the lens. It is found that the lens is a binary composed of two M dwarfs with masses $M_1=0.18pm 0.01 M_odot$ and $M_2=0.16pm 0.01 M_odot$ located at a distance $D_{rm L}= 1.35pm 0.09 {rm kpc}$. According to the estimated lens mass and distance, the flux from the lens comprises an important fraction, $sim 25%$, of the blended flux. The bright nature of the lens combined with the high relative lens-source motion, $mu=6.94pm 0.50 {rm mas} {rm yr}^{-1}$, suggests that the lens can be directly observed from future high-resolution follow-up observations.
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