We report on a combined experimental and theoretical study of the adsorption of the paramagnetic organic radical 2,2,5,5-tetramethyl-3-carboxypyrrolidine nitroxide (3-carboxyproxyl, 3CP) on a Cu(110) surface. Information from scanning tunneling microscopy (STM), reflection absorption infrared spectroscopy, and periodic density functional theory (DFT) calculations reveals important insights into the nature of the molecule-metal interface. We find that the molecule is robustly anchored to the surface via the formation of two Cu-O bonds between the carboxylate functionality and specific short-bridge adsorption sites on the Cu(110) surface. The adsorbed organic radicals appear in STM as discrete entities on the surface and can be imaged with submolecular resolution. We observe a tendency for local 2D ordering. Importantly, 3CP molecules adopt a preferred site, dictated by the strong interaction of the carboxylate groups and the steric repulsion of the methyl groups with the surface which orient the molecular ring almost perpendicular with respect to the surface. This conformation forces the NO radical away from the surface, and DFT calculations provide strong indications for the survival of the unpaired spin localized on the NO radical.