Astronomical observations of elemental and isotopic abundances provide the means to determine the source of elements and to reveal their evolutionary pathways since the formation of the Galaxy some 15 billion years ago. The abundance of lithium is particularly interesting because, although some of it is thought to be primordial, most results from spallation reactions (in which Galactic cosmic rays break apart larger nuclei in the interstellar medium). Spallation reactions are crucial for the production of other light elements, such as beryllium and boron, so observations of lithium isotopic abundances can be used to test model predictions for light-element synthesis in general. Here we report observations of 7Li and 6Li abundances in several interstellar clouds lying in the direction of the star ο Persei. We find the abundance ratio 7Li/6Li to be about 2, which is significantly lower than the average Solar System value of 12.3 (refs 6, 7). An abundance ratio of 2 is clear evidence that the observed lithium must have resulted entirely from spallation, confirming a basic tenet of light-element synthesis. The total lithium abundance, however, is not enhanced as expected.