Monte Carlo simulations are reported of a polymer fluid confined between planar walls using the isotension ensemble, which allows one to perform simulations at constant chemical potential without the necessity of particle exchanges with a bulk polymer fluid. The pressure acting upon the walls and the free energy per unit area of the confined fluid as a function of separation between the walls are obtained, all at constant chemical potential. This is made possible by the use of the so-called free energy difference method. This method appears to be less susceptible to the difficulties that confront the simulation of confined fluids at high density in grand canonical ensemble simulations.