Observations of GRB 100724B with the Fermi Gamma-Ray Burst Monitor (GBM) find that the spectrum is dominated by the typical Band functional form, which is usually taken to represent a non-thermal emission component, but also includes a statistically highly significant thermal spectral contribution . The simultaneous observation of the thermal and non-thermal components allows us to confidently identify the two emission components. The fact that these seem to vary independently favors the idea that the thermal component is of photospheric origin while the dominant non-thermal emission occurs at larger radii. Our results imply either a very high efficiency for the non-thermal process, or a very small size of the region at the base of the flow, both quite challenging for the standard fireball model. These problems are resolved if the jet is initially highly magnetized and has a substantial Poynting flux.