We present the Kepler light curve of KIC 4552982, the first ZZ Ceti (hydrogen-atmosphere pulsating white dwarf star) discovered in the Kepler field of view. Our data span more than 1.5 years, with a 86% duty cycle, making it the longest pseudo-continuous light curve ever recorded for a ZZ Ceti. This extensive data set provides the most complete coverage to date of amplitude and frequency variations in a cool ZZ Ceti. We detect 20 independent frequencies of variability in the data that we compare with asteroseismic models to demonstrate that this star has a mass M * 0.6 > M . We identify a rotationally split pulsation mode and derive a probable rotation period for this star of 17.47 ± 0.04 hr. In addition to pulsation signatures, the Kepler light curve exhibits sporadic, energetic outbursts that increase the star's relative flux by 2%-17%, last 4-25 hr, and recur on an average timescale of 2.7 days. These are the first detections of a new dynamic white dwarf phenomenon that may be related to the pulsations of this relatively cool (T eff 10,860 120 = K) ZZ Ceti star near the red edge of the instability strip.