The use of optical spatial modulation (OSM), which has been recently emerged as a power and bandwidth efficient pulsed modulation technique for indoor optical wireless communication, is proposed as a simple, low-complexity means of achieving spatial diversity in coherent free space optical (FSO) communication systems. In doing so, this paper makes several novel contributions as follows. It presents a generic analytical framework for obtaining the Average Bit Error Probability (ABEP) of uncoded OSM with coherent detection in the presence of turbulence-induced fading. Although the framework is general enough to accommodate any type of models based on turbulence scattering, the focus in this paper is the H-K distribution. Although this distribution represents a very general scattering model valid over a wide range of atmospheric conditions, it is has not been considered in the past in conjunction with FSO systems possibly because of its mathematical complexity. The proposed analytical framework yields exact performance evaluation results for MIMO systems with two transmit- and an arbitrary number of receive apertures. In addition, tight upper bounds are derived for the error probability for OSM systems with an arbitrary number of transmit apertures as well as for convolutionally encoded signals. The performance of OSM is compared to that of well established coherent FSO schemes, employing spatial diversity at the transmitter or the receiver only. Specifically, it is shown that OSM can offer comparable performance with conventional coherent FSO schemes while outperforming the latter in terms of spectral efficiency and hardware complexity. Various numerical performance evaluation results are also presented and compared with equivalent results obtained by Monte Carlo simulations which verify the accuracy of the derived analytical expressions.