The genomes of multicellular organisms are extensively folded into 3D chromosome territories within the nucleus1. Advanced 3D genome-mapping methods that combine proximity ligation and high-throughput sequencing (such as chromosome conformation capture, Hi-C)2, and chromatin immunoprecipitation techniques (such as chromatin interaction analysis by paired-end tag sequencing, ChIA-PET)3, have revealed topologically associating domains4 with frequent chromatin contacts, and have identified chromatin loops mediated by specific protein factors for insulation and regulation of transcription5–7. However, these methods rely on pairwise proximity ligation and reflect population-level views, and thus cannot reveal the detailed nature of chromatin interactions. Although single-cell Hi-C8 potentially overcomes this issue, this method may be limited by the sparsity of data that is inherent to current single-cell assays. Recent advances in microfluidics have opened opportunities for droplet-based genomic analysis9 but this approach has not yet been adapted for chromatin interaction analysis. Here we describe a strategy for multiplex chromatin-interaction analysis via droplet-based and barcode-linked sequencing, which we name ChIA-Drop. We demonstrate the robustness of ChIA-Drop in capturing complex chromatin interactions with single-molecule precision, which has not been possible using methods based on population-level pairwise contacts. By applying ChIA-Drop to Drosophila cells, we show that chromatin topological structures predominantly consist of multiplex chromatin interactions with high heterogeneity; ChIA-Drop also reveals promoter-centred multivalent interactions, which provide topological insights into transcription.