The structure of the interface of an argonlike fluid in equilibrium with its own vapor at low temperature is studied using molecular dynamics. The longitudinal pair correlations in the interface are found to be consistent with a simply defined ensemble of local thermodynamic states. However, the transverse correlations exhibit very long-range behavior not predicted by straightforward local thermodynamics. These results strongly suggest that the interface is made up of an ensemble of configurations in each of which the transition from liquid to vapor is locally sharp, but that the transition surface fluctuates strongly in space and time.