The hard-sphere Yukawa chain (HSYC) fluid is a simple model for chain fluids and polymers in which each molecule is composed of freely-jointed tangent spheres. The spheres each have a hard core and an attractive interaction, written as a single Yukawa potential or as a sum of Yukawa potentials, We have calculated the phase equilibria and PVT behaviour of the HSYC fluid both theoretically and by Monte Carlo simulation. The theoretical approach is based on the analytic solution of the polymer mean spherical approximation for the HSYC fluid. By comparing the theory and simulation we are able to evaluate the accuracy of the theory. We find that in general the theory performs very well, thus, it provides an analytic route to an equation of state for a well-defined model of chain fluids.