We describe the fabrication and characterization of a nanoelectromechanical (NEM) switch based on carbon nanotubes. Our NEM structure consists of single-walled nanotubes (SWNTs) suspended over shallow trenches in a SiO(2) layer, with a Nb pull electrode beneath. The nanotube growth is done on-chip using a patterned Fe catalyst and a methane chemical vapor deposition (CVD) process at 850 degrees C. Electrical measurements of these devices show well-defined ON and OFF states as a dc bias up to a few volts is applied between the CNT and the Nb pull electrode. The CNT switches were measured to have speeds that are 3 orders of magnitude higher than MEMS-based electrostatically driven switches, with switching times down to a few nanoseconds, while at the same time requiring pull voltages less than 5 V.