Electrical current fluctuation studies are reported for coaxial p-type and n-type single-wall carbon nanotube field-effect transistors (FETs). Abrupt discrete switching of the source-drain current is observed at room temperature. The authors attribute these random telegraph signals to charge fluctuating electron traps near the FET conduction channels. Evolution of the current-switching behavior associated with the occupancy of individual electron traps is demonstrated and analyzed statistically. The result strongly indicates room temperature single charge sensitivity in carbon nanotube FETs, which may offer potential applications for single molecule sensors based on suitably prepared FET devices.