Designed as a high-sensitivity gamma-ray observatory, the Fermi Large Area Telescope is also an electron detector with a large acceptance exceeding 2 m;{2} sr at 300 GeV. Building on the gamma-ray analysis, we have developed an efficient electron detection strategy which provides sufficient background rejection for measurement of the steeply falling electron spectrum up to 1 TeV. Our high precision data show that the electron spectrum falls with energy as E-3.0 and does not exhibit prominent spectral features. Interpretations in terms of a conventional diffusive model as well as a potential local extra component are briefly discussed.