The delivery of extraterrestrial organic molecules to Earth by meteorites may have been important for the origin and early evolution of life. Indigenous amino acids have been found in meteorites-over 70 in the Murchison meteorite alone. Although it has been generally accepted that the meteoritic amino acids formed in liquid water on a parent body, the water in the Murchison meteorite is depleted in deuterium relative to the indigenous organic acids. Moreover, the meteoritical evidence for an excess of laevo-rotatory amino acids is hard to understand in the context of liquid-water reactions on meteorite parent bodies. Here we report a laboratory demonstration that glycine, alanine and serine naturally form from ultraviolet photolysis of the analogues of icy interstellar grains. Such amino acids would naturally have a deuterium excess similar to that seen in interstellar molecular clouds, and the formation process could also result in enantiomeric excesses if the incident radiation is circularly polarized. These results suggest that at least some meteoritic amino acids are the result of interstellar photochemistry, rather than formation in liquid water on an early Solar System body.