The genomes of multicellular organisms are extensively folded into 3D chromosome territories within the nucleus(1). 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 domains(4) with frequent chromatin contacts, and have identified chromatin loops mediated by specific protein factors for insulation and regulation of transcription(5-7). 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-C-8 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 analysis(9) 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.