Strong molecular and aerosol scattering in ultraviolet (UV) wavelengths enable the non-line-of-sight (NLOS) outdoor wireless connectivity which is attractive in many applications due to covertness and security. In the current literature, atmospheric turbulence effects are typically ignored under the assumption of short link distances and clear weather conditions. In this paper, we investigate the performance of multiple-input multiple-output (MIMO) UV systems over turbulence channels. Specifically, we derive bit error rate (BER) expressions over an NLOS UV channel which is modeled as an overlap of two log-normal LOS links. Our results demonstrate that fading variance is scaled by the number of transmitters and receivers and MIMO deployment with proper configurations results in significant BER improvements. Simulation results are further provided to confirm the analytical findings.