We have fabricated a Josephson charge qubit by capacitatively coupling a single-Cooper-pair box (SCB) to an electrometer based upon a single-electron transistor configured for radio-frequency readout (RF-SET). Charge quantization of 2e is observed and microwave spectroscopy is used to extract the Josephson and charging energies of the box. We demonstrate coherent manipulation of the SCB by using very fast DC pulses, and observe quantum oscillations in time of the charge that persist to a few ns. Initial oscillation amplitudes as high as 0.5e are observed, with the reduction from the maximum of 1.0e being understood as an adiabatic effect of the finite risetime of the pulses.