We present measurements of the signal and group velocities for chirped optical pulses propagating through a GaAs cavity. The signal velocity is based on a specified signal-to-noise ratio at the detector. Under our experimental conditions, the chirp substantially modifies the group velocity of the pulse, but leaves the signal velocity unaltered. At unity transmittance, the velocities are equal. In general, when the transmittance is less than unity, the group velocity is faster than the signal velocity. While the group velocity can be negative, the signal velocity is always less than c/n, where c is the speed of light in vacuum and n is the refractive index of GaAs. To our knowledge, this is the first measurement of both the group velocity and the signal velocity in any system.