Chaotic laser has attracted a large amount of attention due to its broad spectrum, noise-like characteristics, and photonic integrated chaotic semiconductor lasers have further expanded the application field of chaotic laser for their small size and stable properties. Therefore, a monolithically integrated laser with a distributed Bragg reflector (DBR) is designed. This proposed chaotic laser consists of a distributed feedback (DFB) laser section, a phase section, and a DBR section. DBR grating can provide wavelength detuning to generate mode beating, which enhances chaotic bandwidth and distributed feedback to suppress time delay signature (TDS). The transmission line laser model (TLLM) of chaotic laser is constructed and chaotic characteristics of the integrated chip are investigated. A chaotic signal with a bandwidth of 12.34 GHz and TDS less than 0.065 is obtained. In addition, a map of dynamic states in the parameter space of phase section current and DBR section current is shown, and a wide range of chaotic regions are obtained. The results show that the broadband chaotic laser with a low TDS can be obtained by controlling the parameters reasonably, which is beneficial to realize the application of chaotic laser.