We present the analysis of OGLE-2016-BLG-0613, for which the lensing light curve appears to be that of a typical binary-lens event with two caustic spikes but with a discontinuous feature on the trough between the spikes. We find that the discontinuous feature was produced by a planetary companion to the binary lens. We find 4 degenerate triple-lens solution classes, each composed of a pair of solutions according to the well-known wide/close planetary degeneracy. One of these solution classes is excluded due to its relatively poor fit. For the remaining three pairs of solutions, the most-likely primary mass is about $M_1sim 0.7,M_odot$ while the planet is a super-Jupiter. In all cases the system lies in the Galactic disk, about half-way toward the Galactic bulge. However, in one of these three solution classes, the secondary of the binary system is a low-mass brown dwarf, with relative mass ratios (1 : 0.03 : 0.003), while in the two others the masses of the binary components are comparable. These two possibilities can be distinguished in about 2024 when the measured lens-source relative proper motion will permit separate resolution of the lens and source.
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