Gamma-ray bursts (GRBs) are highly energetic explosions signaling the death of massive stars in distant galaxies. The Gamma-ray Burst Monitor and Large Area Telescope onboard the Fermi Observatory together record GRBs over a broad energy range spanning about 7 decades of gamma-ray energy. In September 2008, Fermi observed the exceptionally luminous GRB 080916C, with the largest apparent energy release yet measured. The high-energy gamma rays are observed to start later and persist longer than the lower energy photons. A simple spectral form fits the entire GRB spectrum, providing strong constraints on emission models. The known distance of the burst enables placing lower limits on the bulk Lorentz factor of the outflow and on the quantum gravity mass.