By solving the time-dependent Schrödinger equation for the Cs atom, we find that, as long as the spectral bandwidth is sufficiently broad, the asymmetry of photoelectron ejection is strongly phase dependent and persists even when the chirped pulse duration becomes more than several cycles. The asymmetry survives even after the angle integration over the hemisphere, implying that the detection efficiency can be significantly improved. This counterintuitive and robust finding provides a simple way to measure the phase for both transform-limited and chirped pulses.