This paper proposes a hybrid time-slot selection-carrier and reference index modulated differential chaos shift keying (HTCR-DCSK) system, aiming to enhance data rate and spectral efficiency under low complexity. At the transmitter, multiple orthogonal chaotic signals are generated by applying circular shifts to the original chaotic sequence, and a Kronecker product is used to extend the original signal. Active and inactive subcarriers are distinguished using the original and shifted chaotic sequences, respectively. Time-slot selection indexing is applied on both active and inactive subcarriers to implicitly transmit additional information bits. At the receiver, denoising is performed on the reference signal to reduce the impact of noise. In addition, the system is analyzed in terms of data rate, spectral efficiency, energy efficiency, and system complexity, and compared with benchmark DCSK systems. Monte Carlo simulations are conducted to evaluate the bit error rate (BER) performance under both additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The simulation results validate the accuracy of the theoretical analysis and demonstrate the superiority of the proposed HTCR-DCSK system in terms of BER performance over benchmark DCSK schemes.