We propose and experimentally study a coherent optical chaotic secure transmission system through a multi-core fiber (MCF). The messages are encrypted by the chaotic carrier and transmitted through the outer cores of the MCF, whereas the chaotic carrier signal is concealed by transmitting through the center core. The MCF provides large transmission capacity expansion and security enhancement against eavesdroppers due to its physical structure. In addition, the designed optical chaos self-homodyne coherent detection strategy has high detection sensitivity and simple physical structure. Due to the prevalence of devices and digital signal processing (DSP) algorithms used in this system, it can be well compatible with a commercial coherent optical communication system. Error free 40 Gb/s/core encrypted 16 quadrature amplitude modulation (QAM) signal transmission over 10 km 7-core fiber is achieved, and 20 Gb/s quadrature phase shift keying (QPSK) signal transmission over a 100 km standard single-mode fiber (SSMF) is demonstrated to verify the long-distance transmission capability. The sensitivity to the secret key is also studied.