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 in single cells is not understood. To address this we developed Tri-C, a new chromosome conformation capture (3C) approach, to characterize concurrent chromatin interactions at individual alleles. Analysis by Tri-C identifies heterogeneous patterns of single-allele interactions between CTCF boundary elements, indicating that the formation of chromatin domains likely results from a dynamic process. Within these domains, we observe specific higher-order structures that involve simultaneous interactions between multiple enhancers and promoters. Such regulatory hubs provide a structural basis for understanding how multiple cis-regulatory elements act together to establish robust regulation of gene expression.