The movement of liquid drops on a surface with a radial surface tension gradient is described here. When saturated steam passes over a colder hydrophobic substrate, numerous water droplets nucleate and grow by coalescence with the surrounding drops. The merging droplets exhibit two-dimensional random motion somewhat like the Brownian movements of colloidal particles. When a surface tension gradient is designed into the substrate surface, the random movements of droplets are biased toward the more wettable side of the surface. Powered by the energies of coalescence and collimated by the forces of the chemical gradient, small drops (0.1 to 0.3 millimeter) display speeds that are hundreds to thousands of times faster than those of typical Marangoni flows. This effect has implications for passively enhancing heat transfer in heat exchangers and heat pipes.