Chaotic optical communication has attracted much attention as a hardware encryption method in the physical layer. Limited by the requirements of chaotic hardware synchronization, fiber transmission impairments are restrictedly compensated in the optical domain. There has been little experimental demonstration of high-speed and long-distance chaotic optical communication systems. Here, we propose a method to overcome such limitations. Using a deep-learning model to realize chaotic synchronization in the digital domain, fiber transmission impairments can be compensated by digital-signal processing (DSP) algorithms with coherent detection. A successful transmission of 30 Gb/s quadrature phase-shift keying messages hidden in a 15 GHz wideband chaotic optical carrier was experimentally demonstrated over a 340-km fiber link. Meanwhile, the chaotic receiver can be significantly simplified without compromising security. The proposed method is a possible way to promote the practical application of chaotic optical communications.