In this paper, we design a novel Poisson photon-counting based iterative successive interference cancellation (SIC) scheme for transmission over free-space optical (FSO) channels in the presence of both multiple access interference (MAI) as well as Gamma-Gamma atmospheric turbulence fading, shot-noise and background light. Our simulation results demonstrate that the proposed scheme exhibits a strong MAI suppression capability. Importantly, an order of magnitude of BER improvements may be achieved compared to the conventional chip-level optical code-division multiple-access (OCDMA) photon-counting detector.