A new wireless transmission scheme, named by authors as beam index modulation (BIM), is proposed in this paper. It exploits radiation beam indices at the transmitter sides to convey information bits, in addition to the information transmitted by modulating radio frequency (RF) carriers, i.e., the classical means of wireless transmission. Favourably, only a single RF chain is required at both transmitter and receiver sides. When compared with traditional beamforming, the proposed BIM system exhibits improved bit error rate (BER) performance in sparse non-Line-of-Sight (nLoS) wireless propagation channels. A parametric study is conducted, from which the design guidelines are provided and experimentally validated.