Comets are known to harbour simple ices and the organic precursors of the building blocks of proteins--amino acids--that are essential to life. Indeed, glycine, the simplest amino acid, was recently confirmed to be present on comet 81P/Wild-2 from samples returned by NASA's Stardust spacecraft. Impacts of icy bodies (such as comets) onto rocky surfaces, and, equally, impacts of rocky bodies onto icy surfaces (such as the jovian and saturnian satellites), could have been responsible for the manufacture of these complex organic molecules through a process of shock synthesis. Here we present laboratory experiments in which we shocked ice mixtures analogous to those found in a comet with a steel projectile fired at high velocities in a light gas gun to test whether amino acids could be produced. We found that the hypervelocity impact shock of a typical comet ice mixture produced several amino acids after hydrolysis. These include equal amounts of D- and L-alanine, and the non-protein amino acids α-aminoisobutyric acid and isovaline as well as their precursors. Our findings suggest a pathway for the synthetic production of the components of proteins within our Solar System, and thus a potential pathway towards life through icy impacts.