The interaction of CO with the Fe3O4(001)-(root 2 x root 2)R45 degrees surface was studied using temperature-programmed desorption (TPD), scanning tunneling microscopy (STM), and X-ray photoelectron spectroscopy (XPS), the latter both under ultrahigh vacuum (UHV) conditions and in CO pressures up to 1 mbar. In general, the COFe3O4 interaction is found to be weak. The strongest adsorption occurs at surface defects, leading to small TPD peaks at 115, 130, and 190 K. Desorption from the regular surface occurs in two distinct regimes. For coverages up to two CO molecules per (root 2 x root 2)R45 degrees unit cell, the desorption maximum shows a large shift with increasing coverage, from initially 105 to 70 K. For coverages between 2 and 4 molecules per (root 2 x root 2)R45 degrees unit cell, a much sharper desorption feature emerges at similar to 65 K. Thermodynamic analysis of the TPD data suggests a phase transition from a dilute 2D gas into an ordered overlayer with CO molecules bound to surface Fe3+ sites. XPS data acquired at 45 K in UHV are consistent with physisorption. Some carbon-containing species are observed in the near-ambient-pressure XPS experiments at room temperature but are attributed to contamination and/or reaction with CO with water from the residual gas. No evidence was found for surface reduction or carburization by CO molecules.