An expression is derived for the pressure dependence of a chemical activation unimolecular rate constant at a fixed total energy and angular momentum in terms of the distribution of unimolecular lifetimes. This rate constant is shown to have a certain insensitivity at low pressures to the form of the lifetime distribution. A kinetic model is then introduced based on a finite rate of intramolecular vibrational energy redistribution. The model provides an analytical explanation of a recent finding in a trajectory calculation for a particular chemical activation system, that the chemical activation unimolecular rate constant at low pressures equals the τ = 0 microcanonical value even though the unimolecular lifetime distribution is highly non-RRKM. A similar result is predicted for a class of such systems. Implications are described.