The Galactic disk retains vast amount of information about how it came to be and how it evolved over cosmic time. However, we know very little about the secular processes associated with disk evolution. One major uncertainty is the extent to which stars migrate radially through the disk, thereby washing out signatures of their past (e.g., birth sites). Recent theoretical work finds that such "blurring" of the disk can be important if spiral arms are transient phenomena. Here we describe an experiment to determine the importance of diffusion from the Solar circle with cosmic time. Consider a star cluster that has been placed into a differentially rotating, stellar fluid. We show that all clusters up to ~10^4 M sun in mass, and a significant fraction of those up to ~10^5 M sun, are expected to be chemically homogeneous, and that clusters of this size can be assigned a unique "chemical tag" by measuring the abundances of l~10 independent element groups, with better age and orbit determinations allowing fewer abundance measurements. The star cluster therefore acts like a "tracer dye," and the present-day distribution of its stars provides a strong constraint on the rate of radial diffusion or migration in the Galactic disk. A star cluster of particular interest for this application is the "Solar family"—the stars that were born with the Sun. If we were able to identify a significant fraction of these, we could determine whether the Sun was born at its present radius or much further in. We show all-sky projections for the Solar family under different dynamical scenarios and identify the most advantageous fields on the sky for the experiment. Sellwood & Binney have argued for strong radial transport driven by transient spiral perturbations: in principle, we could measure the strength of this migration directly. In searching for the Solar family, we would also identify many thousands of other chemically homogeneous groups, providing a wealth of additional information. We discuss this prospect in the context of the upcoming HERMES high-resolution million-star survey.