Stimulated, coherent transition radiation (STR) has been observed at the Stanford SUNSHINE facility. Far-infrared light pulses of coherent transition radiation emitted from femtosecond electron bunches are recycled in a special cavity to arrive back at the radiator coincident with subsequent incoming electron bunches. This overlap enables the electrons to do work on the electromagnetic field, thus stimulating the emission of more radiated energy than would be possible without this external field. The experimental setup to observe STR via cavity detuning measurements and experimental results is discussed. {copyright} {ital 1996 The American Physical Society.}