We describe an approach to detect the frequency of interaction between any two genomic loci. Generation of a matrix of interaction frequencies between sites on the same or different chromosomes reveals their relative spatial disposition and provides information about the physical properties of the chromatin fiber. This methodology can be applied to the spatial organization of entire genomes in organisms from bacteria to human. Using the yeast Saccharomyces cerevisiae, we could confirm known qualitative features of chromosome organization within the nucleus and dynamic changes in that organization during meiosis. We also analyzed yeast chromosome III at the G1 stage of the cell cycle. We found that chromatin is highly flexible throughout. Furthermore, functionally distinct AT- and GC-rich domains were found to exhibit different conformations, and a population-average 3D model of chromosome III could be determined. Chromosome III emerges as a contorted ring.