We present an analysis of the starspots on the active M4 dwarf GJ 1243 , using four years of time series photometry from Kepler . A rapid P = 0.592596 \pm 0.00021 day rotation period is measured due to the \sim 2.2 % starspot-induced flux modulations in the light curve . We first use a light curve modeling approach , using a Monte Carlo Markov Chain sampler to solve for the longitudes and radii of the two spots within 5-day windows of data . Within each window of time the starspots are assumed to be unchanging . Only a weak constraint on the starspot latitudes can be implied from our modeling . The primary spot is found to be very stable over many years . A secondary spot feature is present in three portions of the light curve , decays on 100-500 day timescales , and moves in longitude over time . We interpret this longitude shearing as the signature of differential rotation . Using our models we measure an average shear between the starspots of 0.0047 rad day ^ { -1 } , which corresponds to a differential rotation rate of \Delta \Omega = 0.012 \pm 0.002 rad day ^ { -1 } . We also fit this starspot phase evolution using a series of bivariate Gaussian functions , which provides a consistent shear measurement . This is among the slowest differential rotation shear measurements yet measured for a star in this temperature regime , and provides an important constraint for dynamo models of low mass stars .