We explore the use of tidal streams from Galactic satellites to recover the potential of the Milky Way. Our study is motivated both by the discovery of the first lengthy stellar stream in the halo (cite{it98}) and by the prospect of measuring proper motions of stars brighter than 20th magnitude in such a stream with an accuracy of $sim 4mu as/$yr, as will be possible with the Space Interferometry Mission (SIM). We assume that the heliocentric radial velocities of these stars can be determined from supporting ground-based spectroscopic surveys, and that the mass and phase-space coordinates of the Galactic satellite with which they are associated will also be known to SIM accuracy. Using results from numerical simulations as trial data sets, we find that, if we assume the correct form for the Galactic potential, we can predict the distances to the stars as a consequence of the narrow distribution of energy expected along the streams. We develop an algorithm to evaluate the accuracy of any adopted potential by requiring that the satellite and stars recombine within a Galactic lifetime when their current phase-space coordinates are integrated backwards. When applied to a four-dimensional grid of triaxial logarithmic potentials, with varying circular velocities, axis ratios and orientation of the major-axis in the disk plane, the algorithm can recover the parameters used for the Milky Way in a simulated data set to within a few percent using only 100 stars in a tidal stream.
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