We report on the first time-resolved phase measurement on self-amplified spontaneous emission (SASE) free-electron laser (FEL) pulses. We observed that the spikes in the output of such free-electron laser pulses have an intrinsic positive chirp. We also observed that the energy chirp in the electron bunch mapped directly into the FEL output. Under certain conditions, the two chirps cancel each other. The experimental result was compared with simulations and interpreted with SASE theory.