© 2017. The American Astronomical Society. All rights reserved.. 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 four 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 , while the planet is a super Jupiter. In all cases, the system lies in the Galactic disk, about halfway 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.