We present the discovery that ASASSN-14ko is a periodically flaring active galactic nucleus at the center of the galaxy ESO 253-G003. At the time of its discovery by the All-Sky Automated Survey for Supernovae (ASAS-SN), it was classified as a supernova close to the nucleus. The subsequent 6 yr of V- and g-band ASAS-SN observations revealed that ASASSN-14ko has nuclear flares occurring at regular intervals. The 17 observed outbursts show evidence of a decreasing period over time, with a mean period of P-0 = 114.2 0.4 days and a period derivative of P = -0.0017 +/- 0.003 . The most recent outburst in 2020 May, which took place as predicted, exhibited spectroscopic changes during the rise and had a UV bright, blackbody spectral energy distribution similar to tidal disruption events (TDEs). The X-ray flux decreased by a factor of 4 at the beginning of the outburst and then returned to its quiescent flux after similar to 8 days. The Transiting Exoplanet Survey Satellite observed an outburst during Sectors 4-6, revealing a rise time of 5.60 0.05 days in the optical and a decline that is best fit with an exponential model. We discuss several possible scenarios to explain ASASSN-14ko's periodic outbursts, but currently favor a repeated partial TDE. The next outbursts should peak in the optical on UT 2020 September 7.41.1 and UT 2020 December 26.51.4.