To improve the data rate in differential chaos shift keying (DCSK) based ambient backscatter communication (AmBC) system, we propose a new AmBC system based on code index modulation (CIM), referred to as CIM-DCSK-AmBC system. In the proposed system, the CIM-DCSK signal transmitted in the direct link is used as the radio frequency source of the backscatter link. The signal format in the backscatter link is designed to increase the data rate as well as eliminate the interference of the direct link signal. As such, the direct link signal and the backscatter link signal can be received and demodulated simultaneously. Moreover, we derive and validate the theoretical bit error rate (BER) expressions of the CIM-DCSK-AmBC system over multipath Rayleigh fading channels. Regarding the short reference DCSK-based AmBC (SR-DCSK-AmBC) system as a benchmark system, numerical results reveal that the CIM-DCSK-AmBC system can achieve better BER performance in the direct link and higher throughput in the backscatter link than the benchmark system.