Child prodigies are rare individuals with an exceptional working memory and unique attentional skills that may facilitate the attainment of professional skill levels at an age well before what is observed in the general population. Some characteristics of prodigy have been observed to be quantitatively similar to those observed in autism spectrum disorder (ASD), suggesting possible shared etiology, though objectively validated prodigies are so rare that evidence has been sparse. We performed a family-based genome-wide linkage analysis on 5 nuclear and extended families to search for genetic loci that influence the presence of both prodigy and ASD, assuming that the two traits have the same genetic etiology in the analysis model in order to find shared loci. A shared locus on chromosome 1p31-q21 reached genome-wide significance with two extended family-based linkage methods consisting of the Bayesian PPL method and the LOD score maximized over the trait parameters (i.e., MOD), yielding a simulation-based empirical significance of p = 0.000742 and p = 0.000133, respectively. Within linkage regions, we performed association analysis and assessed if copy number variants could account for the linkage signal. No evidence of specificity for either the prodigy or the ASD trait was observed. This finding suggests that a locus on chromosome 1 increases the likelihood of both prodigy and autism in these families.