In this paper, we present a new multi-antenna modulation scheme, termed as {\em space-time index modulation (STIM)}. In STIM, information bits are conveyed through antenna indexing in the spatial domain, slot indexing in the time domain, and $M$-ary modulation symbols. A time slot in a given frame can be used or unused, and the choice of the slots used for transmission conveys slot index bits. In addition, antenna index bits are conveyed in every used time slot by activating one among the available antennas. $M$-ary symbols are sent on the active antenna in a used time slot. We study STIM in a cyclic-prefixed single-carrier (CPSC) system in frequency-selective fading channels. It is shown that, for the same spectral efficiency, STIM can achieve better performance compared to conventional orthogonal frequency division multiplexing (OFDM). Low-complexity iterative algorithms for the detection of large-dimensional STIM signals are also presented.