Abstract : We measured separate cosmic-ray electron and positron spectra with the Fermi Large Area Telescope. Because the instrument does not have an onboard magnet, we distinguish the two species by exploiting the Earth's shadow, which is offset in opposite directions for opposite charges due to the Earth's magnetic field. We estimate and subtract the cosmic-ray proton background using two different methods that produce consistent results. We report the electron-only spectrum, the positron-only spectrum, and the positron fraction between 20 GeV and 200 GeV. We confirm that the fraction rises with energy in the 20--100 GeV range and determine for the first time that it continues to rise between 100 and 200 GeV.