We have discovered a dwarf nova (DN) of type SU UMa in Kepler data which is 7.0 arcsec from the G-type exoplanet survey target KIC 4378554. The DN appears as a background source in the pixel aperture of the foreground G star. We extracted only the pixels where the DN is present and observed the source to undergo five outbursts – one a superoutburst – over a time span of 22 months. The superoutburst was triggered by a normal outburst, a feature that has been seen in all DNe superoutbursts observed by Kepler. Superhumps during the superoutburst had a period of 1.842 ± 0.004 h, and we see a transition from disc-dominated superhump signal to a mix of disc and accretion stream impact. Predictions of the number of DNe present in Kepler data based on previously published space densities vary from 0.3 to 258. An investigation of the background pixel targets would lead to firmer constraints on the space density of DNe.