Biological macromolecules can condense into liquid domains. In cells, these condensates form membraneless organelles that can organize chemical reactions1,2. However, little is known about the physical consequences of chemical activity in and around condensates. Working with model bovine serum albumin (BSA) condensates 3 , we show that droplets swim along chemical gradients. Active BSA droplets loaded with urease swim toward each other. Passive BSA droplets show diverse responses to externally applied gradients of the enzyme’s substrate and products. In all these cases, droplets swim toward solvent conditions that favor their dissolution. We call this behavior dialytaxis , and expect it to be generic, as conditions which favor dissolution typically reduce interfacial tension, whose gradients are well-known to drive droplet motion4,5. These results suggest alternative physical mechanisms for active transport in living cells, and may enable the design of fluid micro-robots.