We present a photonic method for the generation of dual-chirp signals. In this approach, a single-tone RF signal is first modulated using a modulator in order to generate two optical carriers, which are further modulated by a linearly chirped signal by another modulator. Square-law detection in a photodiode then generates a dual-chirp signal whose center frequency and time-bandwidth product (TBWP) are fourfold increased. The dual-chirping and the improved TBWP can improve the range resolution of the radar system and help avoid the range measurement error caused by the range-Doppler coupling effect. The generation of bandwidth-quadrupled S-band dual-chirp waveforms is demonstrated experimentally. The processing of the dual-chirp signal is also discussed, in order to show its advantages over single-chirp signals. We believe that the proposed approach is a potential solution for the generation of dual-chirp signals with high center frequency and large bandwidth in modern radar systems.