As a first step towards understanding the morphology of PdO crystals we performed a systematic full-potential density-functional theory study of all possible $(1\ifmmode\times\else\texttimes\fi{}1)$ terminations of the low-index surfaces of tetragonal PdO. Applying the concept of first-principles atomistic thermodynamics we analyze the composition, structure and stability of these PdO orientations in equilibrium with an arbitrary oxygen environment. Within the studied subset of $(1\ifmmode\times\else\texttimes\fi{}1)$ geometries the polar PdO-terminated PdO(100) orientation turns out to be surprisingly stable over the whole range of experimentally accessible gas phase conditions. Setting up a constrained Wulff construction within the compiled data set, this PdO(100)-PdO facet correspondingly dominates the obtained polyhedron by far. The real PdO crystallite shape will however likely be affected by surface reconstructions, which are not covered by the present study.