The permeability of oxygen through membranes of poly(cyclohexyl acrylate) at temperatures in the vicinity of the glass transition temperature (T(g)) is determined using an electrochemical experiment. The diffusion coefficient of the gas follows Arrhenius behaviour with an activation energy of 22 kcal mol-1, a surprisingly high value if it is considered that the range of activation energies observed in most systems is 1-20 kcal mol-1. The interpretation of the free volume of the membrane at T(g) suggests that the critical volume necessary for permeation of the gas to take place is nearly four times lower than the value of this parameter for the mechanical and dielectric processes. It is suggested that bulky side groups may aid the transport of gas in the glassy state but presumably hinder it in the rubbery state.