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 $4.3\pm0.2\times10^{37}\,{\rm erg\,s^{-1}}$, and a total integrated energy of $1.27\pm0.01\times10^{43}\,{\rm erg}$. 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$$2\times10^{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.

For decades optical time-domain searches have been tuned to find ordinary supernovae, which rise and fall in brightness over a period of weeks. Recently, supernova searches have improved their cadences and a handful of fast-evolving luminous transients (FELTs) have been identified. FELTs have peak luminosities comparable to Type Ia supernovae, but rise to maximum in <10 days and fade from view in <month. Here we present the most extreme example of this class thus far, KSN2015K, with a rise time of only 2.2 days and a time above half-maximum (t_1/2) of only 6.8 days. Here we show that, unlike Type Ia supernovae, the light curve of KSN2015K was not powered by the decay of radioactive elements. We further argue that it is unlikely that it was powered by continuing energy deposition from a central remnant (a magnetar or black hole). Using numerical radiation hydrodynamical models, we show that the light curve of KSN2015K is well fit by a model where the supernova runs into external material presumably expelled in a pre-supernova mass loss episode. The rapid rise of KSN2015K therefore probes the venting of photons when a hypersonic shock wave breaks out of a dense extended medium.