Chitin is an abundant biopolymer that stabilizes the exoskeleton of insects and gives structure to plants. Its macroscopic properties go back to an intricate network of hydrogen bonds that connect the polymer strands, and these intermolecular links have been under ongoing study. Here, we use atomistic simulations to explore hydrogen bonding in the most abundant form, alpha-chitin. The crystal structure exhibits disorder, and so discrete models are systematically derived as suitable approximants to the macroscopic material. These models then allow us to perform dispersion-corrected density-functional theory (DFT-D) simulations on the three-dimensional crystal network and on lower-dimensional fragments. Thereby, we rationalize the nature of hydrogen bonding and the role of crystallographic disorder for the stability of alpha-chitin, and complement previous, larger-scale molecular-dynamics (MD) simulations as well as recent fiber-diffraction experiments. Our results provide new, atomic-level insight into one of Nature's most abundant building materials, and the techniques and concepts are likely transferable to other biopolymers.