We study the feasibility of generating photon pairs in a resonant Vertical-Cavity Surface-Emitting Laser (VCSEL) as a result of a third-order non-linear, four wave mixing interaction. We focus on degenerate four wave mixing in the spontaneous regime where two pump photons are annihilated to create a pair of signal and idler photons. Using the methods of quantum optics, we calculate the two-photon production rate, the spectrum of the generated photons, and the signal-idler cross-correlations. We highlight how the dispersion of the medium in the VCSEL cavity (a regular GaAs configuration) significantly diminishes the two-photon production rate. Based on our results, we enumerate the characteristics of a VCSEL that would be suitable for photon pair generation.