Mesoscale anticyclonic eddies dominate the sea-surface height variability in the Caribbean Sea. Although it is well established that these anticyclones are formed near the eastern boundary of the Caribbean Sea, which is demarcated by the Lesser Antilles, the source of their anticyclonic vorticity remains unclear. To gain insight into this source, we analyze the fluxes of vorticity into the Caribbean at its eastern boundary using a high-resolution numerical model. We find that the anticyclonic vorticity in the eastern Caribbean Sea predominantly originates from regions where intense ocean currents flow close to the Lesser Antilles. More specifically, St. Lucia and Grenada are hotspots for vorticity generation. The local generation rate scales with the amplitude of the volume transport through the passages between these islands. This finding is in contrast with the view that anticyclonic North Brazil Current (NBC) rings in the Atlantic Ocean are the main source of anticyclonic vorticity in the eastern Caribbean Sea. Our analyses reveal that the direct contribution of the vorticity of the NBC rings is of lesser importance than the local generation. However, the collision of upstream NBC rings with the Lesser Antilles increases the volume transport through the passages into the Caribbean Sea, so that their presence indirectly leads to enhanced local production of anticyclonic vorticity. This process is an example of the importance of vorticity generation near topography, which is ubiquitous in the oceans, and expected to be important whenever currents and steep topography meet.