We report on a study of eclipse timing variations in contact binary systems, using long-cadence lightcurves in the Kepler archive. As a first step, 'observed minus calculated' (O − C) curves were produced for both the primary and secondary eclipses of some 2000 Kepler binaries. We find ∼390 shortperiod binaries with O − C curves that exhibit (i) random-walk like variations or quasi-periodicities, with typical amplitudes of ±200-300 seconds, and (ii) anticorrelations between the primary and secondary eclipse timing variations. We present a detailed analysis and results for 32 of these binaries with orbital periods in the range of 0.35 ± 0.05 days. The anticorrelations observed in their O − C curves cannot be explained by a model involving mass transfer, which among other things requires implausibly high rates of ∼0.01 M ⊙ yr −1 . We show that the anticorrelated behavior, the amplitude of the O − C delays, and the overall random-walk like behavior can be explained by the presence of a starspot that is continuously visible around the orbit and slowly changes its longitude on timescales of weeks to months. The quasi-periods of ∼50 − 200 days observed in the O − C curves suggest values for k, the coefficient of the latitude dependence of the stellar differential rotation, of ∼0.003−0.013.