We evaluate the ensemble averaged noise in a chaotic quantum dot subject to dc bias and a periodic perturbation of frequency \(\Omega\). The noise displays cusps at bias \(V_n=n\hbar \Omega/e\) that survive the average, even when the period of the perturbation is far shorter than the dwell time in the dot. These features are sensitive to the phase of the time-dependent scattering amplitudes of electrons to pass through the system, and thus provide a novel signature of phase-coherent transport that persists into the nonadiabatic limit.