A three-dimensional inviscid velocity distribution is selected to mimic the flow produced at the wall by a three-dimensional vortex convected above an infinite wall. The main interest is in determining the viscous response of the boundary layer on the wall to the imposed pressure distribution. It is demonstrated that complex effects occur in the boundary layer (including the formation of zones of apparent recirculation) that eventually lead to separation. Solutions are obtained in both a conventional Eulerian frame of reference and with a three-dimensional Lagrangian method. The separation takes the form of a sharply focused eruptive tongue of fluid in a manner consistent with modern asymptotic theories of three-dimensional separation, which indicate the boundary-layer solution will develop a singularity in the absence of interaction with the external flow. The unsteady separation structure is similar to that in two dimensions when viewed in the appropriate direction. The possible relevance of the results to the dynamics of turbulent boundary layers is described.