A high‐data‐rate differential chaos shift keying (DCSK) scheme based on spatial modulation (SM), spatially modulated DCSK (SM‐DCSK), is proposed. By employing multiple transmit antennas and using transmit antenna index as information‐carrying unit, the proposed scheme offers a higher data rate compared with the conventional DCSK scheme. In particular, with two transmit antennas, the proposed scheme transmits a DCSK modulated bit from a selected antenna and hence can double the data rate. At the receiver, the maximum received signal is used to retrieve the block of transmitted bits. Mathematical expression for the conditional error probability of the proposed system is derived based on Gaussian approximation. The error probability of the antenna number estimation and the error probability of the transmitted bit estimation are evaluated numerically. Symbol error rate of the proposed scheme is compared with that of the quadrature chaos shift keying scheme. Numerical and simulation results are presented as a function of system parameters.