Chaotic optical communications were originally proposed to provide high-level physical layer security for optical communications. Limited by the difficulty of chaos synchronization, there has been little experimental demonstration of high-speed chaotic optical communications, and point to multipoint chaotic optical networking is hard to implement. Here, we propose a method to overcome the current limitations. By using a deep-learning-based scheme to learn the complex nonlinear model of the chaotic transmitter, wideband chaos synchronization can be realized in the digital domain. Therefore, the chaotic receiver can be significantly simplified while still guaranteeing security. A successful transmission of 32 Gb/s messages hidden in a wideband chaotic optical carrier was experimentally demonstrated over a 20 km fiber link. We believe the proposed deep-learning-based chaos synchronization method will enable a new direction for further development of high-speed chaotic optical communication systems and networks.