We prove that with high probability over the choice of a random graph G from the Erdos-Renyi distribution G(n, 1/2), the n(O(d))-time degree d Sum-of-Squares semidefinite programming relaxation for the clique problem will give a value of at least n(1/2-c(d/log n) 1/2) for some constant c >0. This yields a nearly tight n(1/2-o(1)) bound on the value of this program for any degree d = o(log n). Moreover we introduce a new framework that we call pseudo-calibration to construct Sum-of-Squares lower bounds. This framework is inspired by taking a computational analogue of Bayesian probability theory. It yields a general recipe for constructing good pseudo-distributions (i.e., dual certificates for the Sum-of-Squares semidefinite program), and sheds further light on the ways in which this hierarchy differs from others.