We propose boosted dark matter (BDM) as a possible explanation for the excess of keV electron recoil events observed by XENON1T. BDM particles have velocities much larger than those typical of virialized dark matter, and, as such, BDM-electron scattering can naturally produce keV electron recoils. We show that the required BDM-electron scattering cross sections can be easily realized in a simple model with a heavy vector mediator. Though these cross sections are too large for BDM to escape from the Sun, the BDM flux can originate from the Galactic Center or from halo dark matter annihilations. Furthermore, a daily modulation of the BDM signal will be present, which could not only be used to differentiate it from various backgrounds, but would also provide important directional information for the BDM flux.