Plastics and spilled oil pose a critical threat to marine life and human health. As a result of wind forcing and wave motions, theoretical and laboratory studies predict very strong velocity variation with depth over the upper few centimeters of the water column, an observational blind spot in the real ocean. Here we present the first-ever ocean measurements of the current vector profile defined to within 1 cm of the free surface. In our illustrative example, the current magnitude averaged over the upper 1 cm of the ocean is shown to be nearly four times the average over the upper 10 m, even for mild forcing. Our findings indicate that this shear will rapidly separate pieces of marine debris which vary in size or buoyancy, making consideration of these dynamics essential to an improved understanding of the pathways along which marine plastics and oil are transported.