We have carried out first-principles total-energy calculations of bulk and (001) surfaces of PbZrO3. The ground state for bulk PbZrO3 is determined to be the antiferroelectric orthorhombic phase, with the ferroelectric rhombohedral and paraelectric cubic phases being 0.14 and 0.39 eV per formula unit higher in energy, respectively. PbO- and ZrO2-terminated (001) surfaces, either clean or when hydroxyl species were adsorbed were considered. Surface relaxations, in-plane antiferroelectric distortions and modifications to the electronic structure due to the surfaces, and hydroxyl adsorbates on the surfaces were investigated. We find that while clean surfaces retained bulk-like behavior, hydroxyl adsorbates induce significant changes to the surface geometry as well as introduce electronic states in the band gap possibly rendering the surfaces metallic.