We have measured the angular dependence of chemical bonding forces between a carbon monoxide molecule that is adsorbed to a copper surface and the terminal atom of the metallic tip of a combined scanning tunneling microscope and atomic force microscope. We provide tomographic maps of force and current as a function of distance that revealed the emergence of strongly directional chemical bonds as tip and sample approach. The force maps show pronounced single, dual, or triple minima depending on the orientation of the tip atom, whereas tunneling current maps showed a single minimum for all three tip conditions. We introduce an angular dependent model for the bonding energy that maps the observed experimental data for all observed orientations and distances.