Understanding the physics of low-dimensional systems and the operation of next-generation electronics will depend on our ability to measure the electrical properties of nanomaterials at terahertz frequencies ( similar to 100 GHz to 10 THz). Single-walled carbon nanotubes are prototypical one-dimensional nanomaterials because of their unique band structure(1,2) and long carrier mean free path(3-5). Although nanotube transistors have been studied at microwave frequencies ( 100 MHz to 50 GHz) (6-11), no techniques currently exist to probe their terahertz response(12). Here, we describe the first terahertz electrical measurements of single-walled carbon nanotube transistors performed in the time domain. We observe a ballistic electron resonance that corresponds to the round-trip transit of an electron along the nanotube with a picosecond-scale period. The electron velocity is found to be constant and equal to the Fermi velocity, showing that the high-frequency electron response is dominated by single-particle excitations rather than collective plasmon modes. These results demonstrate a powerful new tool for directly probing picosecond electron motion in nanostructures.