  We have fabricated a Josephson charge qubit by capacitively 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 perform coherent manipulation of the SCB
by using very fast DC pulses and observe quantum oscillations in time of the
charge that persist to ~=10ns. The observed contrast of the oscillations is
high and agrees with that expected from the finite E_J/E_C ratio and finite
rise-time of the DC pulses. In addition, we are able to demonstrate nearly 100%
initial charge state polarization. We also present a method to determine the
relaxation time T_1 when it is shorter than the measurement time T_{meas}.
