Chemical ordering in face-centered-cubic-like PdPt nanoparticles consisting of 38-201 atoms is studied via density-functional calculations combined with a symmetry orbit approach. It is found that for larger particles in the Pd-rich regime, Pt atoms can segregate at the center of the nanoparticle (111) surface facets, in contrast with extended systems in which Pd is known to segregate at the surface of alloy planar surfaces. In a range of compositions around 1:1, a novel multishell chemical ordering pattern was favored, in which each shell is a patchwork of islands of atoms of the two elements, but the order of the patchwork is reversed in the alternating shells. These findings are rationalized in terms of coordination-dependent bond-energy variations in the metal-metal interactions, and their implications in terms of properties and applications of nanoscale alloy particles are discussed.