(Abridged) We present a new high-resolution (7 km/s FWHM) echelle spectrum of 3C 351 obtained with STIS. 3C 351 lies behind the low-latitude edge of high-velocity cloud Complex C, and the new spectrum provides accurate measurements of O I, Si II, Al II, Fe II, and Si III absorption lines at the velocity of the HVC. We use collisional and photoionization models to derive ionization corrections; in both models we find that the overall metallicity Z = 0.1 - 0.3 Z_{solar} in Complex C, but nitrogen must be underabundant. The iron abundance indicates that Complex C contains very little dust. The absorbing gas probably is not gravitationally confined. The gas could be pressure-confined by an external medium, but alternatively we may be viewing the leading edge of the HVC, which is ablating and dissipating as it plunges into the Milky Way. O VI column densities observed with FUSE toward nine QSOs/AGNs behind Complex C support this conclusion: N(O VI) is highest near 3C 351, and the O VI/H I ratio increases substantially with decreasing latitude, suggesting that the lower-latitude portion of the cloud is interacting more vigorously with the Galaxy. The other sight lines through Complex C show some dispersion in metallicity, but with the current uncertainties, the measurements are consistent with a constant metallicity throughout the HVC. However, all of the Complex C sight lines require significant nitrogen underabundances. Finally, we compare the 3C 351 sight line to the sight line to the nearby QSO H1821+643 to search for evidence of outflowing Galactic fountain gas that could be mixing with Complex C. We find that the intermediate-velocity gas detected toward 3C 351 and H1821+643 has a higher metallicity and may well be a fountain/chimney outflow from the Perseus spiral arm.
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