Abstract: Two-neutrino double electron capture is a rare nuclear decay where two electrons are simultaneously captured from the atomic shell. For Xe-124 this process has not yet been observed and its detection would provide a new reference for nuclear matrix element calculations. We have conducted a search for two-neutrino double electron capture from the K shell of 124Xe using 7636 kg d of data from the XENON100 dark matter detector. Using a Bayesian analysis we observed no significant excess above background, leading to a lower 90% credibility limit on the half-life T-1/2 > 6.5 x 10(20) yr. We have also evaluated the sensitivity of the XENON1T experiment, which is currently being commissioned, and found a sensitivity of T-1/2 > 6.1 x 10(22) yr after an exposure of 2 t yr.