We demonstrate a tunnel field-effect transistor based on a lateral heterostructure patterned from an LaAlO3/SrTiO3 electron gas. Charge is injected by tunneling from the LaAlO3/SrTiO3 contacts and the current through a narrow channel of insulating SrTiO3 is controlled via an electrostatic side gate. Drain-source I-V curves are measured at low and elevated temperatures. The transistor shows strong electric-field-dependent and temperature-dependent behavior, with a steep subthreshold slope as small as 10mV/dec and a transconductance as high as approximately 22μA/V. A fully consistent transport model for the drain-source tunneling reproduces the measured steep subthreshold slope.