In field-effect transistors (FETs), charge trapping in the gate oxide is known to cause low-frequency noise and threshold shifts. Here we calculate the effect of single trapped charges in a carbon nanotube FET, using the nonequilibrium Greens function method in a tight-binding approximation. We find that a single charge can shift and even rescale the entire transfer characteristic of the device. This can explain both the large "random telegraph signal" noise and the large variations between nominally identical devices. We examine the dependence on both the thickness and dielectric constant of the gate dielectric, suggesting routes to reduce electrical noise.