The authors report on the fabrication and characteristics of a unipolar, three-terminal, resonant-tunneling transistor. The operating principle of this new transistor is based on the fact that the quantum mechanical resonant-tunneling probability of hot electrons between the emitter and the collector is switched almost completely on and off, when either the base or the collector bias is swept. The emitter injects hot electrons to the second lowest subband of a thin (100 AA in this work) GaAs quantum well. Subsequently, the hot electrons will either resonantly tunnel to the collector, or relax to the lowest subband and contribute to the base current. As a result of resonant transmission, at 77 K the current-voltage characteristics of the transistor display negative differential resistance with extremely large (4691) peak-to-valley ratio. Furthermore, when biased near resonance, a maximum DC current gain of approximately 1.2 and a maximum AC current gain of approximately 11.9 were observed. The first use of a new 'tunneling-in and tunneling-out' scheme in contacting a thin quantum well is also demonstrated. >