We propose a method to generate broadband laser chaos using a quantum cascade laser (QCL). Through numerical simulation, we give the evidence that the QCL with optical feedback can route to chaos through the quasi-periodic path. Furthermore, we investigate the influence of the feedback intensity and the bias current on the chaos bandwidth. Final results demonstrate that the chaos bandwidth can headily reach 43.1 GHz due to the lack of relaxation oscillation phenomena in QCLs.