Molecular dynamics simulations are used to probe the atomic-scale behavior of a model for a self-assembled monolayer of n-hexadecanethiol chemisorbed on a gold (111) surface compressed under high loads. These simulations suggest that SAMs may undergo abrupt rearrangements during compression that retain efficient packings of the chains. These changes may in turn modify the elastic properties of the films without chain entanglement or film destruction. We propose that the signature of such a transition is visible in a force profile recently measured by Joyce et al. (Phys. Rev. Lett. 1992, 68, 2790) with an interfacial force microscope.