This paper investigates the opportunity for a repetition coded multi-carrier index keying-orthogonal frequency division multiplexing (MCIK-OFDM), termed repeated MCIK-OFDM (ReMO), which can provide superior performance over existing schemes at the same spectral efficiency. Unlike the classical scheme, the proposed scheme activates a subset of subcarriers and modulates them with the same M-ary data symbol, while additional information is conveyed by the active sub-carrier indices. This approach not only provides the frequency diversity gains in the M-ary symbol detection but also improves the index detection, leading to considerable improvement in the transmit diversity. For performance analysis, we derive tight closed-form expressions for the symbol error probability and the bit error rate, under both perfect and imperfect channel state information (CSI). These expressions provide insight into the achievable performance gains, system designs, and impacts of various CSI conditions. Finally, simulation results are given to illustrate the superior performance achieved by our scheme over existing schemes under different CSI uncertainties.