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) x unk M unk, and the complex represents a mass inflow of 0.1-0.25 M unk yr-1. We base our distance bracket on the detection of Ca II absorption in the spectrum of the blue horizontal branch (BHB) star SDSS J120404.78+623345.6, in combination with a significant nondetection 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.