We present the earliest ultraviolet (UV) observations of the bright Type Ia supernova SN 2011fe/PTF11kly in the nearby galaxy M101 at a distance of only 6.4 Mpc. It was discovered shortly after explosion by the Palomar Transient Factory and first observed by Swift/UVOT about a day after explosion. The early UV light is well-defined, with ~20 data points per filter in the five days after explosion. These early and well-sampled UV observations form new template light curves for comparison with observations of other SNe Ia at low and high redshift. We report fits from semi-empirical models of the explosion and find the time evolution of the early UV flux to be well fit by the superposition of two parabolic curves. Finally, we use the early UV flux measurements to examine a possible shock interaction with a non-degenerate companion. From models predicting the measurable shock emission, we find that even a solar mass companion at a distance of a few solar radii is unlikely at more than 95% confidence. ; Comment: Manuscript expanded and modified following the referee's report. Resubmitted to ApJ