GRB110721A was observed by the Fermi Gamma-ray Space Telescope using its two instruments, the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM). The burst consisted of one major emission episode which lasted for ~24.5 s (in the GBM) and had a peak flux of (5.7 ± 0.2) × 10–5 erg s–1 cm–2. The time-resolved emission spectrum is best modeled with a combination of a Band function and a blackbody spectrum. The peak energy of the Band component was initially 15 ± 2 MeV, which is the highest value ever detected in a GRB. This measurement was made possible by combining GBM/BGO data with LAT Low Energy events to achieve continuous 10-100 MeV coverage. The peak energy later decreased as a power law in time with an index of –1.89 ± 0.10. The temperature of the blackbody component also decreased, starting from ~80 keV, and the decay showed a significant break after ~2 s. The spectrum provides strong constraints on the standard synchrotron model, indicating that alternative mechanisms may give rise to the emission at these energies.