How did the first cells on Earth arise? In a minimal cell, a membrane separates proteins and RNA from the surrounding aqueous environment. Cell-like membranes spontaneously assemble from simple prebiotic surfactants called fatty acids. However, fatty acid membranes are unstable in solutions containing salts that were likely present in environments of the early Earth. We find that amino acids, the building blocks of proteins, bind to fatty acid membranes and stabilize them against salts. Moreover, enhanced stabilization persists after dilution as would occur when a dehydrated pool refills with water—a likely setting for the emergence of cells. In addition to explaining how the first membranes were stabilized, our findings answer how key components of the first cells colocalized.