A dual mode index and time diversity based differential chaos shift keying (DM-TD-DCSK) scheme is proposed. In this scheme, all carriers excepting the reference carrier are divided into two classes by the index bits, and then the first active carriers are utilized to transmit the first modulated bits and the second active carriers are utilized to transmit the second modulated active bits. Time diversity is also employed to deal with the noise of the power line channel, where the transmitted signals are sent in different intervals and averaged at the receiver. The bit error rate expression is derived over the power line channel and validated through Monte Carlo simulations. Both theoretical analysis and simulated results demonstrate the superiority of the proposed scheme. Combining with diversity and index modulation, DM-TD-DCSK not only enhances the spectral efficiency and energy efficiency of the system compared to the traditional index modulation in which active carriers transmit modulation bits while inactive carriers transmit no information, but also effectively mitigates the impact of impulse noise over power line channels. However, the complexity of the transceivers increases due to employing the two technologies, and thus, the DM-TD-DCSK scheme improves system performance at the cost of higher system complexity.