Semiconductor lasers with delayed optical feedback are a promising source of optical chaos for practical applications, owing to simple configurations that are easy to integrate and synchronize. However, for traditional semiconductor lasers, the chaos bandwidth is limited by the relaxation frequency to several gigahertz. Here, we propose and experimentally demonstrate that a short-resonant-cavity distributed-feedback (SC-DFB) laser can generate broadband chaos only with simple feedback from an external mirror. The short distributed-feedback resonant cavity not only enhances laser relaxation frequency but also makes the laser mode more susceptible to external feedback. Experiments obtained a laser chaos with 33.6 GHz bandwidth and a spectral flatness of 4.5 dB. The corresponding entropy rate is estimated as more than 33.3 Gbit/s. It is believed that the SC-DFB lasers will promote development of chaos-based secure communication and physical key distribution.