Over the past decade, 3C-related methods, complemented by increasingly detailed microscopic views of the nucleus, have provided unprecedented insights into chromosome folding in vivo. Here, to overcome the resolution limits inherent to the majority of genome-wide chromosome architecture mapping studies, we extend a recently-developed Hi-C variant, Micro-C, to map chromosome architecture at nucleosome resolution in human embryonic stem cells and fibroblasts. Micro-C maps robustly capture well-described features of mammalian chromosome folding including A/B compartment organization, topologically associating domains (TADs), and cis interaction peaks anchored at CTCF binding sites, while also providing a detailed 1-dimensional map of nucleosome positioning and phasing genome-wide. Compared to high-resolution in situ Hi-C, Micro-C exhibits substantially improved signal-to-noise with an order of magnitude greater dynamic range, enabling not only localization of domain boundaries with single-nucleosome accuracy, but also resolving more than 20,000 additional looping interaction peaks in each cell type. Intriguingly, many of these newly-identified peaks are localized along stripe patterns and form transitive grids, consistent with their anchors being pause sites impeding the process of cohesin-dependent loop extrusion. Together, our analyses provide the highest resolution maps of chromosome folding in human cells to date, and provide a valuable resource for studies of chromosome folding mechanisms.