Abstract Supercoiling impacts DNA replication, transcription, protein binding to DNA, and the three-dimensional organization of chromosomes. However, there are currently no methods to directly interrogate or map positive supercoils, so their distribution in genomes remains unknown. Here, we describe a method, GapR-seq, based on the chromatin immunoprecipitation of GapR, a bacterial protein that preferentially recognizes overtwisted DNA, for generating high-resolution maps of positive supercoiling. Applying this method to E. coli and S. cerevisiae , we find that positive supercoiling is widespread, associated with transcription, and particularly enriched between convergently-oriented genes, consistent with the “twin-domain” model of supercoiling. In yeast, we also find positive supercoils associated with centromeres, cohesin binding sites, autonomously replicating sites, and the borders of R-loops (DNA-RNA hybrids). Our results suggest that GapR-seq is a powerful approach, likely applicable in any organism, to investigate aspects of chromosome structure and organization not accessible by Hi-C or other existing methods.