Magnetic domain structures are active electron transport agents and can be used to induce large magnetoresistance (MR), particularly in half-metallic solids. We have studied the excess resistance induced by a single magnetic domain wall in a one-dimensional half-metallic CrO₂ nanoscale conductor with a built-in constriction whose channel width (d) ranges from 30 to 200 nm. We observed that the domain wall-induced MR is enhanced by 70 fold when d decreases from 200 nm to 30 nm. We speculate that the enhancement is due to the increased domain wall resistance (DWR) and the extra contribution of ballistic magnetoresistance (BMR). We have uncovered a large size effect of d on the MR induced by the domain wall, which scales with d as d^{−1.87±0.32}. Accordingly, we predict that the MR ratio of a simple CrO₂ nanowire impregnated with a constriction at a 150 nm² cross-section could reach 100%. This large MR far exceeds that of a conventional ferromagnetic nanowire, confirming the role of half metallicity on enhanced magneto-transport.