We present a new geometrical method for measuring the distance to the Galactic center (r0) by solving for the Keplerian orbit of individual stars bound to the black hole associated with the Sgr A* from radial velocity and proper motion measurements. We identify three stars to which the method may be applied, and show that 1-5% accuracy of r0 can be expected fter 15 years of observing, and 0.5-2% after 30 years of observing, depending on what the orbital parameters of these three stars turn out to be. Combining the measurements of the three stars with favorable orbital parameters leads to even more precise values. In the example that we present, such combined solution yields 4% accuracy already by the year 2002. All these estimates assume that annual position measurements will continue to be made with the sigmarho = 2 mas precision recently reported by Ghez et al. The precision of the distance measurement is relatively insensitive to the radial velocity errors, provided that the latter are less than 50 km/sec . Besides potentially giving an estimate of r0 that is better than any currently in use, the greatest advantage of this method is that it is free from systematic errors.