We present an exquisite 30 minute cadence Kepler (K2) light curve of the Type Ia supernova (SN Ia) 2018oh (ASASSN-18bt), starting weeks before explosion, covering the moment of explosion and the subsequent rise, and continuing past peak brightness. These data are supplemented by multi-color Panoramic Survey Telescope (Pan-STARRS1) and Rapid Response System 1 and Cerro Tololo Inter-American Observatory 4 m Dark Energy Camera (CTIO 4-m DECam) observations obtained within hours of explosion. The K2 light curve has an unusual two-component shape, where the flux rises with a steep linear gradient for the first few days, followed by a quadratic rise as seen for typical supernovae (SNe) Ia. This "flux excess" relative to canonical SN Ia behavior is confirmed in our i-band light curve, and furthermore, SN 2018oh is especially blue during the early epochs. The flux excess peaks 2.14 ± 0.04 days after explosion, has a FWHM of 3.12 ± 0.04 days, a blackbody temperature of K, a peak luminosity of , and a total integrated energy of . We compare SN 2018oh to several models that may provide additional heating at early times, including collision with a companion and a shallow concentration of radioactive nickel. While all of these models generally reproduce the early K2 light curve shape, we slightly favor a companion interaction, at a distance of ∼ based on our early color measurements, although the exact distance depends on the uncertain viewing angle. Additional confirmation of a companion interaction in future modeling and observations of SN 2018oh would provide strong support for a single-degenerate progenitor system.