We present the first ab initio simulation of a reversible addition fragmentation chain transfer (RAFT) polymerization. Using ab initio molecular orbital theory, we calculate the equilibrium constants for the first eight addition-fragmentation steps in the cyanoisopropyl dithiobenzoate-mediated polymerization of styrene. We then simulate the concentration profiles for the RAFT agent, and its unimeric and dimeric adducts, assuming standard experimental parameters for styrene homopolymerization and the addition of the styryl radical to the RAFT agent. The simulated data show excellent agreement with published experimental data, highlighting the accuracy of quantum chemistry. In contrast, the currently used chain-length independent models fail to describe even the qualitative trends in the data, regardless of whether the fragmentation reaction is assumed to be fast or slow. The calculated chain-length dependent equilibrium constants are large, in agreement with the earlier proposed slow fragmentation model.