  We report an accurate distance of d = 10+/-2.5kpc to the high-velocity cloud
Complex C. Using high signal-to-noise Keck/HIRES spectra of two
horizontal-branch stars, we have detected CaII K absorption lines from the
cloud. Significant non-detections toward a further 3 stars yield robust lower
distance limits. The resulting HI mass of Complex C is 4.9^{+2.8}_{-2.2} x 10^6
Msun; a total mass of 8.2^{+4.6}_{-2.6} x 10^6 Msun is implied, after
corrections for helium and ionization. At 10kpc, Complex C has physical
dimensions 3x15 kpc, and if it is as thick as it is wide, then the average
density is log<n> ~ -2.5. We estimate the contribution of Complex C to the mass
influx may be as high as ~0.14 Msun/yr.
