Although the molecular rules governing genome organization are being quickly elucidated, relatively few proteins regulating this process have been identified. To address this gap, we developed a fully automated imaging pipeline, called HiDRO (high-throughput DNA or RNA labeling with optimized Oligopaints), that permits quantitative measurement of chromatin interactions across a large number of samples. Using HiDRO, we screened the human druggable genome and identified >300 factors that regulate chromatin folding during interphase, including 43 validated hits that either increase or decrease interactions between topological associating domains (TADs). We discovered that genetic or chemical inhibition of the ubiquitous kinase GSK3A enhances long-range interactions by dysregulating cohesin-mediated chromatin looping. Collectively, these results highlight a noncanonical role for GSK3A signaling in nuclear architecture and underscore the broader utility of HiDRO-based screening to identify novel mechanisms that drive the spatial organization of the genome.