Recent decades have witnessed remarkable and continuing improvements in the performance of field-effect transistors (FETs). These improvements result largely from aggressive scaling of devices to smaller sizes. As further improvement of conventional FETs becomes increasingly difficult, attention has focused on new devices like carbon nanotube (CN) FETs. CNFETs have already shown very promising performance, despite the use of relatively thick gate oxides [1–3]. Here we examine the performance improvement of CNFETs upon scaling of the thickness and dielectric constant of the gate oxide. In both experimental measurements and numerical calculations, we find a very different scaling behavior than for conventional transistors, with important consequences for the design of CNFETs. Specifically, we find that key measures of device performance scale approximately as the square root of the gateoxide thickness tox or its inverse. These include the turnon voltage, the transconductance, and the subthreshold slope. We show that this surprising behavior can be captured in a simple analytic model, which gives a universal form for the saturation current versus gate voltage. Our model incorporates the recent recognition [1,2,4–6] that, in ambipolar CNFETs such as ours, transistor action is caused by modulation of the Schottky barriers (SBs) at the metal-nanotube contacts. The model also highlights the central role of the contact geometry in determining the scaling, with different geometries giving different power laws for the scaling. In contrast, the scaling of conventional FETs with tox is independent of contact geometry in the long-channel limit.