Hydrogen-vacancy complexes can form in a material due to the exothermic binding of hydrogen atoms to vacancy sites. We explore the structure and electronic properties of hydrogen-vacancy complexes in delta-Pu using a density functional theory supercell approach, with up to eight hydrogen atoms stored in the vacancy site. We find that the hydrogen atoms bind to the inner edge of the vacancy site, preferring pseudo-octahedral configurations that optimize the Pu-H bond length. Hydrogen binding to the vacancy site remains exothermic, with binding energies around -0.4 eV/H atom. A statistical mechanics analysis is derived and applied to reveal the range of hydrogen chemical potentials that would lead to hydrogen-vacancy complex formation. We find that these chemical potentials are higher than those required to form the hydride phase, indicating that hydriding should occur before any appreciable concentration of vacancy-hydrogen complexes is realized. Some remarks are made comparing this theoretical finding to the experimental work on this topic, with suggestions given for future work that may help reconcile some apparent contradictions.