We demonstrate radio frequency single-electron transistors fabricated from epitaxially grown InAs/InP heterostructure nanowires. Two sets of double-barrier wires with different barrier thicknesses were grown. The wires were suspended 15 nm above a metal gate electrode. Electrical measurements on a high-resistance nanowire showed regularly spaced Coulomb oscillations at a gate voltage from −0.5 to at least 1.8 V. The charge sensitivity was measured to 32 µerms Hz−1/2 at 1.5 K. A low-resistance single-electron transistor showed regularly spaced oscillations only in a small gate-voltage region just before carrier depletion. This device had a charge sensitivity of 2.5 µerms Hz−1/2. At low frequencies this device showed a typical 1/f noise behavior, with a level extrapolated to 300 µerms Hz−1/2 at 10 Hz.