We describe chirped-pulse generation from an optical parametric oscillator using an aperiodic quasi-phase-matching crystal as the gain medium. We examine the pulse formation dynamics, and reveal that the excitation of chirped-pulse oscillation is assisted by the position-dependent conversion-wavelength and the pump-to-signal temporal walk-off along the gain medium. Stable oscillation is confirmed by numerical simulations and experimental demonstrations. In a preliminary experiment, we obtained a signal wave covering 1293–1734 nm and an idler wave covering 2.9–5.0 µm from an oscillator based on a 2-mm-long aperiodically poled LiNbO3 crystal. These results represent a new, to the best of our knowledge, pulse formation mechanism inside a nonlinear oscillator, which is promising for generating light pulses with very wide instantaneous bandwidth and at arbitrary wavelengths.