Current understanding of chromosome folding is largely reliant on chromosome conformation capture (3C)-based experiments, where chromosomal interactions are detected as ligation products after chromatin crosslinking. To measure chromosome structure in vivo, quantitatively and without crosslinking and ligation, we implemented a modified version of DNA adenine methyltransferase identification (DamID) named DamC, which combines DNA methylation-based detection of chromosomal interactions with next-generation sequencing and biophysical modeling of methylation kinetics. DamC performed in mouse embryonic stem cells provides the first in vivo validation of the existence of topologically associating domains (TADs), CTCF loops and confirms 3C-based measurements of the scaling of contact probabilities. Combining DamC with transposon-mediated genomic engineering shows that new loops can be formed between ectopic and endogenous CTCF sites, which redistributes physical interactions within TADs. DamC provides the first crosslinking- and ligation-free demonstration of the existence of key structural features of chromosomes and provides novel insights into how chromosome structure within TADs can be manipulated.