This paper presented very early, high-cadence photometric observations of the nearby Type Ia SN 2017cbv. The light-curve is unique in that during the first five days of observations it has a blue bump in the U, B, and g bands which is clearly resolved by virtue of our photometric cadence of 5.7 hr during that time span. We modelled the light-curve as the combination of an early shock of the supernova ejecta against a non-degenerate companion star plus a standard Type Ia supernova component. Our best-fit model suggested the presence of a subgiant star 56 R☉ from the exploding white dwarf, although that number is highly model-dependent. While the model matches the optical light-curve well, it over-predicts the flux expected in the ultraviolet bands. That may indicate that the shock is not a blackbody, perhaps because of line blanketing in the UV. Alternatively, it could point to another physical explanation for the optical blue bump, such as interaction with circumstellar material or an unusual distribution of the element Ni. Early optical spectra of SN 2017cbv show strong carbon absorption as far as day -13 with respect to maximum light, suggesting that the progenitor system contained a significant amount of unburnt material. These results for SN 2017cbv illustrate the power of early discovery and intense follow-up of nearby supernovæ for resolving standing questions about the progenitor systems and explosion mechanisms of Type Ia supernovæ.