GALACTIC globular clusters were once thought to be chemically homogeneous, having formed quite rapidly from relatively small condensations of primordial gas(29). In many clusters, significant star-to-star variations in light-element abundances have been observed(1-4) in evolved giant stars. These variations have been attributed to the presence at the stellar surfaces of nucleosynthesis products generated deep within the stars. But other observations(13) have suggested that some of this variability was established earlier in the stars’ lifetimes, perhaps as a result of inhomogeneities in the gas cloud from which the cluster formed. Here we report the observation of variations in the sodium abundances of unevolved (main-sequence) stars in the cluster 47 Tucanae. Although these variations are similar to those observed in evolved cluster stars, they cannot be explained by mixing, in the framework of current models of stellar evolution. This indicates either that the gas out of which 47 Tuc formed was chemically inhomogeneous, or that some mechanism for altering the surface element abundances of stars operates while they are still on the main sequence.