In this paper, we propose a simple transmit diversity scheme for orthogonal frequency division multiplexing (OFDM) with index modulation (IM) in order to achieve a diversity gain for index detection, which can significantly improve the performance of OFDM-IM at the cost of the spectral efficiency. An optimal approach for active index detection is derived, which has a complexity, growing linearly with the size of OFDM symbol. A salient feature of the proposed transmit diversity scheme is that it can be easily employed in conjunction with a conventional coding scheme for data symbols. Consequently, we can implement coded OFDM-IM together with the proposed transmit diversity scheme in a straightforward manner, which can provide a good performance under a frequency-fading environment.