Oceanic Rossby waves have been widely invoked as a mechanism for large-scale variability of chlorophyll (CHL) observed from satellites. High-resolution satellite altimeter measurements have recently revealed that sea-surface height (SSH) features previously interpreted as linear Rossby waves are nonlinear mesoscale coherent structures (referred to here as eddies). We analyze 10 years of measurements of these SSH fields and concurrent satellite measurements of upper-ocean CHL to show that these eddies exert a strong influence on the CHL field, thus requiring reassessment of the mechanism for the observed covariability of SSH and CHL. On time scales longer than 2 to 3 weeks, the dominant mechanism is shown to be eddy-induced horizontal advection of CHL by the rotational velocities of the eddies.