First-principles calculations for the structural, electronic and magnetic properties of clean and CO-adsorbed Ni{110} demonstrate that the spin-structure of the surface depends upon adsorption geometry in a highly localised fashion. The magnetic moments of top-layer atoms are enhanced on the clean surface, and attenuated by CO adsorption. Strikingly, however, the adsorbate-induced demagnetisation is limited primarily to those surface atoms directly bonded to the molecule. The adsorbate itself was found to be only weakly magnetised, in the opposite sense to the surface majority spin.