The promoters of mammalian genes are commonly regulated by multiple distal enhancers, which physically interact within discrete chromatin domains. How such domains form and how the regulatory elements within them interact within single cells is not understood. To address this we developed Tri-C, a new Chromosome Conformation Capture (3C) approach to identify concurrent chromatin interactions at individual alleles within single cells. The heterogeneity of interactions observed between such cells shows that CTCF-mediated formation of chromatin domains and interactions within them are dynamic processes. Importantly, our analyses reveal higher-order structures involving simultaneous interactions between multiple enhancers and promoters within individual cells. This provides a structural basis for understanding how multiple cis-elements act together to establish robust regulation of gene expression.