We report results of a search for light (≲10 GeV) particle dark matter with the XENON10 detector. The event trigger was sensitive to a single electron, with the analysis threshold of 5 electrons corresponding to 1.4 keV nuclear recoil energy. Considering spin-independent dark matter-nucleon scattering, we exclude cross sections σ(n)>7×10(-42) cm(2), for a dark matter particle mass m(χ)=7 GeV. We find that our data strongly constrain recent elastic dark matter interpretations of excess low-energy events observed by CoGeNT and CRESST-II, as well as the DAMA annual modulation signal.