Application of recent geometric tools for Lagrangian coherent structures (LCS) shows that material attraction in geostrophic velocities derived from altimetry data imposed an important constraint to the motion of drifters from the Grand Lagrangian Deployment (GLAD) in the Gulf of Mexico. This material attraction is largely transparent to traditional Eulerian analysis. Attracting LCS acted as approximate centerpieces for mesoscale patterns formed by the drifters. Persistently attracting LCS cores emerged 1 week before the development of a filament resembling the “tiger tail” of the Deepwater Horizon oil slick, thereby anticipating its formation. Our results suggest that the mesoscale circulation plays a significant role in shaping near-surface transport in the Gulf of Mexico.