Gamma-ray bursts are among the most powerful events in nature. These events release most of their energy as photons with energies in the range from 30 keV to a few MeV, with a smaller fraction of the energy radiated in radio, optical, and soft X-ray afterglows. The data are in general agreement with a relativistic shock model, where the prompt and afterglow emissions correspond to synchrotron radiation from shock-accelerated electrons. Here we report an observation of a high-energy (multi-MeV) spectral component in the burst of 17 October 1994 that is distinct from the previously observed lower-energy γ-ray component. The flux of the high-energy component decays more slowly and its fluence is greater than the lower-energy component; it is described by a power law of differential photon number index approximately -1 up to about 200 MeV. This observation is difficult to explain with the standard synchrotron shock model, suggesting the presence of new phenomena such as a different non-thermal electron process, or the interaction of relativistic protons with photons at the source.