Breakthroughs in high-throughput sequencing and microscopic imaging technologies have revealed that chromatin structures vary considerably between cells of the same type. However, a thorough characterization of this heterogeneity remains elusive due to the labor-intensive and time-consuming nature of these experiments. To address these challenges, we introduce ChromoGen, a generative model based on state-of-the-art artificial intelligence techniques that efficiently predicts three-dimensional, single-cell chromatin conformations \emph{de novo} with both region- and cell type-specificity. These generated conformations accurately reproduce experimental results at both the single-cell and population level. Moreover, ChromoGen successfully transfers to cell types excluded from the training data using just DNA sequence and widely available DNase-seq data, thus providing access to chromatin structures in myriad cell types. These achievements come at a remarkably low computational cost. Therefore, ChromoGen enables the systematic investigation of single-cell chromatin organization, its heterogeneity, and its relationship to sequencing data, all while remaining economical.