Competitive adsorption and lateral pressure between surface-bound intermediates are important effects that dictate chemical reactivity. Lateral, or two-dimensional, pressure is known to promote reactivity by lowering energetic barriers and increasing conversion to products. We examined the coadsorption of CO and H2, the two reactants in the industrially important Fischer-Tropsch synthesis, on Co nanoparticles to investigate the effect of two-dimensional pressure. Using scanning tunneling microscopy, we directly visualized the coadsorption of H and CO on Co, and we found that the two adsorbates remain in segregated phases. CO adsorbs on the Co nanoparticles via spillover from the Cu(111) support, and when deposited onto preadsorbed adlayers of H, CO exerts two-dimensional pressure on H, compressing it into a higher-density, energetically less-preferred structure. By depositing excess CO, we found that H on the Co surface is forced to spill over onto the Cu(111) support. Thus, spillover of H from Co onto Cu, where it would not normally reside due to the high activation barrier, is preferred over desorption. We corroborated the mechanism of this spillover-induced displacement by calculating the relevant energetics using density functional theory, which show that the displacement of H from Co is compensated for by the formation of strong CO-Co bonds. These results may have significant ramifications for Fischer-Tropsch synthesis kinetics on Co, as the segregation of CO and H, as well as the displacement of H by CO, limits the interface between the two molecules.