The influence of the small ionic surfactant sodium dodecyl sulfate (SDS) on the evaporation of drying colloidal droplets is quantitatively investigated. The addition of SDS leads to a significantly more uniform deposition of colloidal particles after evaporation (i.e., the so-called "coffee-ring effect" is dramatically altered). We understand this phenomenon in the context of circulating radial Marangoni flows induced by the variation of SDS concentration along the air-water interface. Video microscopy permits the direct visualization of the colloidal particles involved in these flows, revealing a surprisingly stable "Marangoni eddy" that prevents particle deposition at the drop perimeter.