Carbon nanotubes(1) display a consummate blend of materials properties that affect applications ranging from nanoelectronic circuits(2) and biosensors(3) to field emitters(4) and membranes(5). These applications use the non- covalent interactions between the nanotubes and chemical functionalities(6), often involving a few molecules at a time. Despite their wide use, we still lack a fundamental understanding and molecular- level control of these interactions. We have used chemical force microscopy(7) to measure the strength of the interactions of single chemical functional groups with the sidewalls of vapour- grown individual single- walled carbon nanotubes. Surprisingly, the interaction strength does not follow conventional trends of increasing polarity or hydrophobicity, and instead reflects the complex electronic interactions between the nanotube and the functional group. Ab initio calculations confirm the observed trends and predict binding force distributions for a single molecular contact that match the experimental results. Our analysis also reveals the important role of molecular linkage dynamics in determining interaction strength at the single functional group level.