We present the analysis of the gravitational microlensing event OGLE-2013-BLG-0102 . The light curve of the event is characterized by a strong short-term anomaly superposed on a smoothly varying lensing curve with a moderate magnification A _ { max } \sim 1.5 . It is found that the event was produced by a binary lens with a mass ratio between the components of q = 0.13 and the anomaly was caused by the passage of the source trajectory over a caustic located away from the barycenter of the binary . From the analysis of the effects on the light curve due to the finite size of the source and the parallactic motion of the Earth , the physical parameters of the lens system are determined . The measured masses of the lens components are M _ { 1 } = 0.096 \pm 0.013 ~ { } M _ { \odot } and M _ { 2 } = 0.012 \pm 0.002 ~ { } M _ { \odot } , which correspond to near the hydrogen-burning and deuterium-burning mass limits , respectively . The distance to the lens is 3.04 \pm 0.31 ~ { } { kpc } and the projected separation between the lens components is 0.80 \pm 0.08 ~ { } { AU } .