We present microlensing events in the 2015 Korea Microlensing Telescope Network (KMTNet) data and our procedure for identifying these events. In particular, candidates were detected with a novel "completed-event" microlensing event-finder algorithm. The algorithm works by making linear fits to a grid of point-lens microlensing models. This approach is rendered computationally efficient by restricting u0 to just two values (0 and 1), which we show is quite adequate. The implementation presented here is specifically tailored to the commission-year character of the 2015 data, but the algorithm is quite general and has already been applied to a completely different (non-KMTNet) data set. We outline expected improvements for 2016 and future KMTNet data. The light curves of the 660 "clear microlensing" and 182 "possible microlensing" events that were found in 2015 are presented along with our policy for their public release.