We describe a new microlensing-event alert algorithm that is tailored to the Korea Microlensing Telescope Network (KMTNet) multi-observatory system. The algorithm focuses on detecting "rising" events, i.e., events whose brightness is increasing as a function of time. The algorithm proceeds in three steps. It first identifies light curves with at least Nhigh points that are at least 3σ above the median and that had been taken since shortly before the previous search for new events. It then demands that there are at least Nhigh consecutive high points when considering any combination of light curves from one, two, or three observatories. Finally, it fits to a "rising microlensing model" consisting of a broken line, i.e., flat before some time trise and rising linearly afterward. If this fit is better than a flat line by Δχ2>Δχthresh2, the light curve is sent for human review. Here, (Nhigh,Δχthresh2)=(5,250) or (10,400), depending on the field cadence. For 2018, KMTNet alerts will initially be restricted to a few northern bulge fields and may gradually extend to the full northern bulge. Further expansion of coverage is expected in 2019.