Application of dynamical systems tools has recently revealed in surface ocean currents produced by a Hybrid-Coordinate Ocean Model (HYCOM) simulation the presence of a persistent large-scale Lagrangian coherent structure (LCS) on the southern portion of the west Florida shelf (WFS). Consistent with satellite-tracked drifter trajectories, this LCS constitutes a cross-shelf barrier for the lateral transport of passive tracers. Because of the constraints that the above LCS, as well as smaller-scale LCSs lying shoreside, can impose on pollutant dispersal and its potentially very important biological consequences, a study was carried out on the nature of the surface ocean Lagrangian motion on the WFS. The analysis is based on the same simulated surface ocean velocity field that has been able to sustain the aforementioned persistent cross-shelf transport barrier. Examination of several diagnostics suggests that chaotic stirring dominates over turbulent mixing on time scales of up to two months or so. More specifically, it is found on those time scales that tracer evolution at a given length scale is governed to a nonnegligible extent by coarser-scale velocity field features, fluid particle dispersion is spatially inhomogeneous, and the Lagrangian evolution is more irregular than the driving Eulerian flow.