The spatial organization of chromosomes in the nuclear space is an extensively studied field that relies on measurements of structural features and 3D positions of chromosomes with high precision and robustness. However, no tools are currently available to image and analyze chromosome territories in a high-throughput format. Here, we have developed High-throughput Chromosome Territory Mapping (HiCTMap), a method for the robust and rapid analysis of 2D and 3D chromosome territory positioning in mammalian cells. HiCTMap is a high-throughput imaging-based chromosome detection method which enables routine analysis of chromosome structure and nuclear position. Using an optimized FISH staining protocol in a 384-well plate format in conjunction with a bespoke automated image analysis workflow, HiCTMap faithfully detects chromosome territories and their position in 2D and 3D in a large population of cells per experimental condition. We apply this novel technique to visualize chromosomes 18, X, and Y in male and female primary human skin fibroblasts, and show accurate detection of the correct number of chromosomes in the respective genotypes. Given the ability to visualize and quantitatively analyze large numbers of nuclei, we use HiCTMap to measure chromosome territory area and volume with high precision and determine the radial position of chromosome territories using either centroid or equidistant-shell analysis. The HiCTMap protocol is also compatible with RNA FISH as demonstrated by simultaneous labeling of X chromosomes and Xist RNA in female cells. We suggest HiCTMap will be a useful tool for routine precision mapping of chromosome territories in a wide range of cell types and tissues.