The authors present results on the quantum conduction properties of a one-dimensional channel, 0.7 mu m long and 0.3 mu m wide, containing two potential barriers. The barriers are 0.5 mu m apart and 0.18 mu m wide and are defined by a gate on a high-mobility GaAs-AlGaAs heterojunction. The device behaves like a one-dimensional ballistic point contact with two narrow barriers in the middle. Reducing the width by electrostatic squeezing reveals quasi-periodic peaks in the resistance due to the resonance. At higher temperatures the effect of the barriers is removed so that the peaks disappear leaving the quantised plateaus associated with a one-dimensional ballistic point contact. A magnetic field removes the structure when the level broadening becomes comparable to the level separation.