The dynamic three-dimensional spatial conformations of chromosomes demonstrate complex structural variations across single cells, which plays pivotal roles in modulating single-cell specific transcription and epigenetics landscapes. The high rates of missing contacts in single-cell chromatin contact maps impose significant challenges to reconstruct high-resolution spatial chromatin configurations. We develop a data-driven algorithm, Tensor-FLAMINGO, based on a low-rank tensor completion strategy. Implemented on a diverse panel of single-cell chromatin datasets, Tensor-FLAMINGO generates 10kb- and 30kb-resolution spatial chromosomal architectures across individual cells. Tensor-FLAMINGO achieves superior accuracy in reconstructing 3D chromatin structures, recovering missing contacts, and delineating cell clusters. The unprecedented high-resolution characterization of single-cell genome folding enables expanded identification of single-cell specific long-range chromatin interactions, multi-way spatial hubs, and the mechanisms of disease-associated GWAS variants. Beyond the sparse 2D contact maps, the complete 3D chromatin conformations promote an avenue to understand the dynamics of spatially coordinated molecular processes across different cells.