We have used the NRAO Very Long Baseline Array to image water masers associated with the low-luminosity, young stellar object (YSO) IRAS 05413-0104 at four epochs over a period of 10 weeks. The maser images show the detail of a symmetric, jetlike structure about 300 mas in extent. The 23° ± 2° position angle of the maser spot distribution is in excellent agreement with measured position angles for the observed larger scale H₂ and SiO emission distributions; radial velocities are in agreement with SiO measurements showing redshifted gas to the southwest and blueshifted gas to the northeast. We have detected proper motions of numerous maser spots averaging 30 ± 12 mas yr⁻¹, implying space velocities of 64 ± 27 km s⁻¹ for a source distance of 450 pc. Some masers are located within a projected distance of 40 AU of the origin of expansion, the assumed position of the central source, suggesting that jet formation and acceleration takes place within this radius of the YSO. We compute an inclination of the outflow system to the plane of the sky of 4°, based on the relative magnitude of the proper motions and radial velocities of the masers. VLBI observations of water masers in YSOs are clearly demonstrated to be interesting and competitive probes of the kinematics of the gas in YSO jets.