We report the first determination of a distance bracket for the high-velocity cloud (HVC) complex C. Combined with previous measurements showing that this cloud has a metallicity of 0.15 times solar, these results provide ample evidence that complex C traces the continuing accretion of intergalactic gas falling onto the Milky Way. Accounting for both neutral and ionized hydrogen as well as He, the distance bracket implies a mass of 3–14×10 M⊙, and the complex represents a mass inflow of 0.1–0.25 M⊙ yr . We base our distance bracket on the detection of Ca II absorption in the spectrum of the blue horizontal branch star SDSSJ120404.78+623345.6, in combination with a significant non-detection toward the BHB star BS 16034-0114. These results set a strong distance bracket of 3.7–11.2 kpc on the distance to complex C. A more weakly supported lower limit of 6.7 kpc may be derived from the spectrum of the BHB star BS 16079-0017. Department of Astronomy, University of Wisconsin, Madison, WI 53706; wakker@astro.wisc.edu Astronomy & Astrophysics Center, University of Chicago, Chicago, IL 60637; don@oddjob.uchicago.edu Dept. of Physics, University of Notre Dame, Notre Dame, IN 46556; jhowk@nd.edu Dept. of Astronomy, Univ. of Texas, Austin TX 78712 and Apache Point Observatory, Sunspot, NM 88349; jcb@astro.as.utexas.edu Dept. of Physics & Astronomy, Texas Tech University, Lubbock TX 79409; ron.wilhelm@ttu.edu Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 AV, Groningen; peletier@astro.rug.nl, hugo@astro.rug.nl Department of Physics and Astronomy, Michigan State University, CSCE: Center for the Study of Cosmic Evolution and JINA: Joint Institute for Nuclear Astrophysics, Michigan State University, E. Lansing, MI 48824, USA; beers@pa.msu.edu Dept. of Astronomy, University of Washington, Box 351580, Seattle, WA 98195; ivezic@astro.washington.edu Institut für Physik, Universität Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany; prichter@astro.physik.uni-potsdam.de Department of Astrophysics, Radboud University Nijmegen, Toernooiveld 1, NL-6525 ED, The Netherlands; schwarz@kun.nl