The operation of a negative differential conductance (NDC) transistor fabricated on a high-mobility Si/Si1-xGex heterostructure wafer is described. The drain characteristic of this device shows a large NDC with current peak-to-valley ratios as high as 600 (100) at T = 0.4 K (T = 1.3 K). The NDC can be modulated over a wide range of current levels by either of two separately-contacted gate electrodes. The device shows bistable switching behavior in both current- and voltage-controlled circuit configurations. The novel operating principle of this transistor is described, along with its potential for future logic and memory applications.