Large intelligent surfaces arise as an emerging technology and critical building block for sixth generation (6G) wireless networks. Reconfigurable holographic surfaces (RHSs) have been attracting significant attention recently as active antenna arrays with the capability of forming narrow beams at low cost and complexity. This paper introduces the directional modulation (DM) concept for RHS, where a large number of elements is exploited to control not only the signal's power at the receiver but also its phase. Thus, a novel DM algorithm is proposed for RHS enables modulating a carrier wave to transmit information towards specific directions while broadcasting arbitrary signals towards other directions. Error vector magnitude (EVM) results are reported for multiple users, where the directions of two users with respect to the RHS are varied. Mutual information result is also provided for 6 users to demonstrate the application of RHS for the physical layer security. Results are highly promising for future low-cost and secure spatially multiplexed communications.