Quantum theory predicts the existence of the Casimir force between macroscopic bodies, a force arising from the zero-point energy of electromagnetic field modes around them. I will report the experimental observation of the thermal Casimir force between two gold plates, due to thermal rather than quantum fluctuations of the electromagnetic field at room-temperature. The thermal Casimir force dominates over the quantum force for separations greater than a micrometer. We use our measurements to place new upper bounds on short-range exotic forces, arising, for example, in quantum gravity theories with extra dimensions.