We apply our cooperative free volume (CFV) rate model for pressure-dependent dynamics to describe the relaxation times for poly(4-chlorostyrene) (P4ClS) bulk and thin films. The CFV model expresses segmental relaxation times, tau, as a function of temperature, T, and thermodynamic free volume, V-free = V - V-hc, where the limiting hard core volume, V-hc, is obtained via analysis of a polymer's experimental PVT data using the locally correlated lattice (LCL) model equation of state. In adapting CFV to describe thin films, we assume that the main effect of confinement is that the interface serves to change the average free volume (average density) compared to bulk. We formulate a simple weighted average expression (involving just a single interface related parameter) to describe the free volume of a film as a function of thickness, h, and use this h-dependent V-free within the CFV model expression. Using just ambient pressure relaxation time data on bulk P4ClS, along with PVT data, we parametrize the CFV model, which is then able to predict both the P-dependent dynamics for the P4ClS bulk and the thickness-dependent dynamics of P4ClS films; the CFV parameters are transferable for either scenario. Analysis of the bulk P-dependent dynamics predictions for P4ClS indicates a strong sensitivity to volume changes, and this leads to a strong sensitivity to confinement (h). In addition, we show that the effect of confinement, e.g., for a 15 nm P4ClS film, is analogous to the effect of a P decrease on the order of about 25 MPa or so. The model tau vs h behavior is in close agreement with the form of the isothermal experimental data. Furthermore, we show predictions for the film behavior at other temperatures, based on analysis of the limited (T = 433 K) experimental data that are available.