We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A pi/2-gate time of 2.5 ns and a coherence time of 19 mu s, using multipulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment.