We present an exquisite, 30-min 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 Pan-STARRS1 and 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 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$pm0.04$ days after explosion, has a FWHM of 3.12$pm0.04$ days, a blackbody temperature of $T=17,500^{+11,500}_{-9,000}$ K, a peak luminosity of $4.3pm0.2times10^{37},{rm erg,s^{-1}}$, and a total integrated energy of $1.27pm0.01times10^{43},{rm erg}$. 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 $sim$$2times10^{12},{rm cm}$ 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.
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