In this talk, I will present a connection between the Fractional Chromatic Number and the integrality gap of the LP for the Maximum Weight Independent Set. Specifically, the ratio of Fractional Chromatic Number to Clique Number tightly captures the Integrality Gap of the LP with clique constraints for the Maximum Weight Independent Set problem. I will also present immediate applications of our results in approximating the fractional chromatic number of certain classes of intersection graphs.