Chemisorbed p(1\ifmmode\times\else\texttimes\fi{}1) oxygen on ultrathin epitaxial Fe films grown on W(001) are studied using spin- and angle-resolved photoemission. In agreement with theoretical predictions, single-monolayer (ML) Fe films on W(001) are found to be nonmagnetic; 2-ML-thick Fe films are magnetic, and chemisorbed p(1\ifmmode\times\else\texttimes\fi{}1) oxygen does not destroy the magnetism. Even- and odd-symmetry oxygen 2p-derived bands are measured along the \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}-X\ifmmode\bar\else\textasciimacron\fi{} and \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}-M\ifmmode\bar\else\textasciimacron\fi{} directions of the two-dimensional Brillouin zone. Oxygen-derived features in the photoemission spectra exhibit magnetic exchange splitting as well as spin-dependent intrinsic linewidths that are governed by lifetime effects and initial-state mixing with Fe bands. Oxygen 2p-band narrowing resulting from the expanded Fe thin-film lattice constant is observed. The results are compared with relevant calculations and corresponding experimental studies of p(1\ifmmode\times\else\texttimes\fi{}1) oxygen on bulk Fe(001) surfaces.