We present small-angle neutron scattering measurements on the system living poly(alpha-methylstyrene) in deuterated tetrahydrofuran, using sodium naphthalide as the initiator. We study three samples, differing in the ratio, r, of the number of moles of initiator to the number of moles of initial monomer and differing in the mole fraction of initial monomer. We compare the data to a theory for the scattering which treats the polymerization as a phase transition in the mean field approximation and also to a theory based on the dilute n --> 0 magnet model (where n is the dimension of the order parameter) in which no mean field assumption is made but in which an assumption of no solvent interaction is made [Wheeler, J. C.; Pfeuty, P. M. Phys. Rev. Lett. 1993, 71, 1653]. We compare the measured concentration structure function, S(q,T) (where q is the wavenumber and T is the temperature) and S(0,T), the extrapolation to q = 0, to the theoretical predictions. We find that both the mean field theory and the dilute n --> 0 magnet model are able to account qualitatively for the general features of the scattering data. However, the mean field theory does not predict the maximum observed in S(0,T) at temperatures below the polymerization temperature. The maximum in S(0,T) is predicted by the dilute n --> 0 model in its zero solvent interaction limit. We determine also the characteristic length, xi(T), which increases as the living polymers form and grow, reaches a maximum at the temperature at which overlap begins, and then decreases as the polymer mesh develops. Both the mean field theory and the dilute n --> 0 model are in qualitative, but not quantitative, agreement with the measurements of xi(T).