The eukaryotic chromosomes adopt complex and dynamic three-dimensional (3D) folding within cell nucleus, entailing widespread multiway chromatin contacts involving more than two genomic segments. Hi-C and derivative methods only capture pairwise contacts, unable to discover the entirety of multiway contacts. Here we introduce three-way Hi-C (3wHi-C) for profiling contacts among three segments with an equal and fine-scale proximity between any two. 3wHi-C contacts exhibit the best equi-proximity across available multiway methods. By comparing with piled-up pairwise contacts, we demonstrate that three-way chromatin contacts are not spontaneous consequences from the constituent pairwise contacts, but has chromatin context-specific propensities. Furthermore, based on the 3D contact matrix filled with equi-proximal three-way contacts, we identify 3wHi-C specific TAD boundaries resided by evolutionarily young genome features, and distinguish compartment subtypes segregating better under three-way than two-way viewpoint. Finally, we show that three-way chromatin contacts are responsive to DNA damage stimuli, manifested by the damage-induced three-way contact features. In summary, our results suggest that multiway chromatin contact is a prevalent feature of 3D genome folding. The genome folding subtypes specifically resolved by 3wHi-C demonstrate that increasing profiling dimensionality helps unfold chromatin structural features invisible to regular Hi-C profiling.