Curved crystal surfaces enable the systematic and accurate comparison of physical and chemical processes for a full set of vicinal crystal planes, which are probed in the very same environment. Here, we examine the early stages of the CO chemisorption on vicinal Rh(111) surfaces using a curved Rh crystal that exposes a smoothly variable density of {100} (A-type) and {111} (B-type) steps. We readily identify and quanti step and terrace species by resolving their respective core-level lines using X-ray photoelectron spectroscopy at different locations on the curved surface. Uptake experiments show similar sticking probabilities at all surface planes, subtle asymmetries between A- and B-type steps, and significantly lower saturation coverage at densely stepped surfaces as compared to the (111) plane. The analysis of the C is intensity variation across the curved sample allows us to discuss the adsorption geometry around the step edge.