  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 $M_1=0.18\pm 0.01\ M_\odot$ and
$M_2=0.16\pm 0.01\ M_\odot$ located at a distance $D_{\rm L}= 1.35\pm 0.09\
{\rm kpc}$. 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,
$\mu=6.94\pm 0.50\ {\rm mas}\ {\rm yr}^{-1}$, suggests that the lens can be
directly observed from future high-resolution follow-up observations.
