Single (Co/Pt)_{7} multilayer nanowires prepared by electron beam lithography with perpendicular magnetic anisotropy are locally modified by means of Ga-ion implantation generating 180 degrees domain walls which are pinned at the edges of underlying thin Pt wires. Since we can exclude contributions from the anisotropic and the Lorentz magnetoresistance this allows us to determine the resistance of a single domain wall at room temperature. We find a positive relative resistance increase of DeltaR/R=1.8% inside the domain wall which agrees well with the model of Levy and Zhang [Phys. Rev. Lett. 79, 5110 (1997)10.1103/PhysRevLett.79.5110].