The electrical resistance of a conductor is intimately related to the relaxation of the momentum of charge carriers. In a simple model, the accelerating force exerted on electrons by an applied electric field is balanced by a frictional force arising from their frequent collisions with obstacles such as impurities, grain boundaries or other deviations from a perfect crystalline order. Thus, in the absence of any scattering, the electrical resistance should vanish altogether. Here, we observe such vanishing four-terminal resistance in a single-mode ballistic quantum wire. This result contrasts the value of the standard two-probe resistance measurements of h/2e2 approximately 13 kOmega. The measurements are conducted in the highly controlled geometry afforded by epitaxial growth onto the cleaved edge of a high-quality GaAs/AlGaAs heterostructure. Two weakly invasive voltage probes are attached to the central section of a ballistic quantum wire to measure the inherent resistance of this clean one-dimensional conductor.