The growth of vapor-deposited Cr and chromium oxide on Pt(111) has been studied by ion scattering spectroscopy, x-ray photoelectron spectroscopy, low energy electron diffraction, and scanning tunneling microscopy. Both metal Cr film and its oxide nucleate at Pt(111) step edges, and grow in a step-flow mode. The metal Cr film is pseudomorphic to the Pt(111) substrate within the first two monolayers. At higher coverages, the chromium overlayer adopts a bcc(110) surface structure and forms three-dimensional elongated islands oriented along the three close-packed directions of the Pt(111) surface. For the chromium oxide, a well ordered p(2X2) structure is observed within the first two monolayers and attributed to the epitaxial growth of metastable Cr3O4. At higher coverages, a (root 3 X root 3)R30 degrees structure appears, due to the formation of the stable Cr2O3 phase.