A new type of electrometer is described that uses a single-electron transistor (SET) and that allows large operating speeds and extremely high charge sensitivity. The SET readout was accomplished by measuring the damping of a 1.7-gigahertz resonant circuit in which the device is embedded, and in some ways is the electrostatic "dual" of the well-known radio-frequency superconducting quantum interference device. The device is more than two orders of magnitude faster than previous single-electron devices, with a constant gain from de to greater than 100 megahertz. For a still-unoptimized device, a charge sensitivity of 1.2 x 10(-5) e/root hertz was obtained at a frequency of 1.1 megahertz, which is about an order of magnitude better than a typical, 1/f-noise-limited SET,and corresponds to an energy sensitivity (in joules per hertz) of about 41 (h) over bar.