We demonstrate the possibility to run a single-pass free-electron laser in a new dynamical regime, which can be exploited to perform two-colour pump-probe experiments in the VUV/X-ray domain, using the free-electron laser emission both as a pump and as a probe. The studied regime is induced by triggering the free-electron laser process with a powerful laser pulse, carrying a significant and adjustable frequency chirp. As a result, the emitted light is eventually split in two sub-pulses, whose spectral and temporal separations can be independently controlled. We provide a theoretical description of this phenomenon, which is found in good agreement with experiments performed on the FERMI@Elettra free-electron laser.