The asymmetrical positioning of neural structures on the left or right side of the brain in vertebrates^, and in invertebrates^, may be correlated with brain laterality, which is associated with cognitive skills. But until now this has not been illustrated experimentally. Here we describe an asymmetrically positioned brain structure in the fruitfly Drosophila and find that the small proportion of wild-type flies that have symmetrical brains with two such structures lack a normal long-term memory, although their short-term memory is intact. Our results indicate that brain asymmetry may be required for generating or retrieving long-term memory.