We present the results of a search through the photometric database of Kepler eclipsing binaries looking for evidence of hierarchical triple-star systems. The presence of a third star orbiting the binary can be inferred from eclipse timing variations. We apply a simple algorithm in an automated determination of the eclipse times for all 2157 binaries. The "calculated" eclipse times, based on a constant period model, are subtracted from those observed. The resulting O-C (observed minus calculated times) curves are then visually inspected for periodicities in order to find triple-star candidates. After eliminating false positives due to the beat frequency between the similar to 1/2 hr Kepler cadence and the binary period, 39 candidate triple systems were identified. The periodic O-C curves for these candidates were then fit for contributions from both the classical Roemer delay and so-called physical delay, in an attempt to extract a number of the system parameters of the triple. We discuss the limitations of the information that can be inferred from these O-C curves without further supplemental input, e.g., ground-based spectroscopy. Based on the limited range of orbital periods for the triple-star systems to which this search is sensitive, we can extrapolate to estimate that at least 20% of all close binaries have tertiary companions.