We present the first results of searches for axions and axionlike particles with the XENON100 experiment. The axion-electron coupling constant, gAe, has been probed by exploiting the axioelectric effect in liquid xenon. A profile likelihood analysis of 224.6 live days × 34-kg exposure has shown no evidence for a signal. By rejecting gAe larger than 7.7×10-12 (90% C.L.) in the solar axion search, we set the best limit to date on this coupling. In the frame of the DFSZ and KSVZ models, we exclude QCD axions heavier than 0.3 and 80 eV /c2, respectively. For axionlike particles, under the assumption that they constitute the whole abundance of dark matter in our galaxy, we constrain gAe to be lower than 1×10-12 (90% C.L.) for masses between 5 and 10 keV /c2.