Water-soluble polymers such as polyethylene glycol (PEG) are critical components of industrial processes ranging from drug delivery to water purification. However, the understanding of the microscopic structure of these polymers in water and of the thermodynamics of the mixtures is limited because available experimental techniques (such as SLS and SANS) give little information about conformations and provide even the radius of gyration only in the dilute limit (<~5 wt % PEG). Computer simulations employing Monte Carlo (MC) and molecular dynamics (MD) techniques can provide an atomistic molecular structure; however, such approaches have difficulties in predicting the equilibrium polymer configurations of high-molecular-weight polymers at normal densities and in obtaining entropies and free energies directly from the MD. Here, we develop the scaled effective solvent (SES) method to predict the equilibrium ensemble of polymer configurations, which we illustrate for the case of a 20 kDa PEG (455 monomers) at a 25 wt % PEG aqueous solution (3339 waters per PEG chain). We evaluate the free energy and entropy of the members of this ensemble including explicit water, validating that it leads to average sizes (R(g)) observed experimentally and that all members of the ensemble have favorable free energies. With the SES method validated to provide well-equilibrated polymer chains in water, it should be useful for predicting ensembles of polymer chains in polymer melts and in solvents.