Quantitative genetics has primarily focused on describing genetic effects on trait means and largely ignored the effect of alternative alleles on trait variability, potentially missing an important axis of genetic variation contributing to phenotypic differences among individuals. To study the genetic effects on individual-to-individual phenotypic variability (or intragenotypic variability), we used Drosophila inbred lines and measured the spontaneous locomotor behavior of flies walking individually in Y-shaped mazes, focusing on variability in locomotor handedness, an assay optimized to measure variability. We discovered that some lines had consistently high levels of intragenotypic variability among individuals, whereas lines with low variability behaved as although they tossed a coin at each left/right turn decision. We demonstrate that the degree of variability is itself heritable. Using a genome-wide association study (GWAS) for the degree of intragenotypic variability as the phenotype across lines, we identified several genes expressed in the brain that affect variability in handedness without affecting the mean. One of these genes, Ten-a, implicates a neuropil in the central complex of the fly brain as influencing the magnitude of behavioral variability, a brain region involved in sensory integration and locomotor coordination. We validated these results using genetic deficiencies, null alleles, and inducible RNAi transgenes. Our study reveals the constellation of phenotypes that can arise from a single genotype and shows that different genetic backgrounds differ dramatically in their propensity for phenotypic variabililty. Because traditional mean-focused GWASs ignore the contribution of variability to overall phenotypic variation, current methods may miss important links between genotype and phenotype.