We propose and experimentally demonstrate a method of generating wideband and flat-spectrum chaos from a simple device configuration composed of a semiconductor laser subject to strong dispersive light feedback from a chirped fiber Bragg grating (CFBG). The dispersive feedback light induces external-cavity modes with irregular mode separations which beat with the internal modes of laser. This physical process of beating introduces more highfrequency oscillations and thus removes the domination of relaxation oscillation, widening and flattening the radio-frequency spectrum. Experimental results show that laser chaos with a 3-dB bandwidth of 24 GHz can be obtained at a feedback strength of 1.60, which is three times the bandwidth at a feedback strength of 0.35. Effects of the dispersive feedback strength and the wavelength detuning between the laser and the CFBG on the 3-dB bandwidth are studied.