While nuclear compartmentalization is an essential feature of three-dimensional genome organization, no genomic method exists for measuring chromosome distances to defined nuclear structures. In this study, we describe TSA-Seq, a new mapping method capable of providing a “cytological ruler” for estimating mean chromosomal distances from nuclear speckles genome-wide and for predicting several Mbp chromosome trajectories between nuclear compartments without sophisticated computational modeling. Ensemble-averaged results in K562 cells reveal a clear nuclear lamina to speckle axis correlated with a striking spatial gradient in genome activity. This gradient represents a convolution of multiple spatially separated nuclear domains including two types of transcription “hot zones.” Transcription hot zones protruding furthest into the nuclear interior and positioning deterministically very close to nuclear speckles have higher numbers of total genes, the most highly expressed genes, housekeeping genes, genes with low transcriptional pausing, and super-enhancers. Our results demonstrate the capability of TSA-Seq for genome-wide mapping of nuclear structure and suggest a new model for spatial organization of transcription and gene expression.