We present a new theory for the nucleation of gas-phase monomers in a supersaturated vapor on a growing short-chain polymer. Reiss and co-workers have shown that cloud chambers can be extraordinarily sensitive detectors of single molecules of particular size in such experiments, giving valuable information about rate constants for gas-phase polymerization. We have used a density functional approach to calculate the free energy and heterogeneous nucleation rate of liquid drops of monomer on oligomer chains of varying length. We show that the free energy is not a simple monotonic function of chain length as assumed in simple classical theories.