We report on the discovery of ≥100MeV γ-rays from the binary system PSR B1259-63/LS 2883 using the Large Area Telescope (LAT) on board Fermi. The system comprises a radio pulsar in orbit around a Be star. We report on LAT observations from near apastron to ∼128 days after the time of periastron, ∼tp , on 2010 December 15. No γ-ray emission was detected from this source when it was far from periastron. Faint γ-ray emission appeared as the pulsar approached periastron. At ∼tp + 30 days, the ≥100MeV γ-ray flux increased over a period of a few days to a peak flux 20-30 times that seen during the pre-periastron period, but with a softer spectrum. For the following month, it was seen to be variable on daily timescales, but remained at ∼(1-4) × 10-6 cm-2 s-1 before starting to fade at ∼tp + 57 days. The total γ-ray luminosity observed during this period is comparable to the spin-down power of the pulsar. Simultaneous radio and X-ray observations of the source showed no corresponding dramatic changes in radio and X-ray flux between the pre-periastron and post-periastron flares. We discuss possible explanations for the observed γ-ray-only flaring of the source. © 2011. The American Astronomical Society. All rights reserved.