  We present the detection of dust depletion in Complex C, a massive,
infalling, low-metallicity high-velocity cloud in the northern Galactic
hemisphere that traces the ongoing accretion of gas onto the Milky Way. We
analyze a very high signal-to-noise HST/COS spectrum of AGN Mrk 817 formed by
coadding 165 individual exposures taken under the AGN STORM 2 program, allowing
us to determine dust-depletion patterns in Complex C at unprecedented
precision. By fitting Voigt components to the O I, S II, N I, Si II, Fe II, and
Al II absorption and applying ionization corrections from customized Cloudy
photoionization models, we find sub-solar elemental abundance ratios of
[Fe/S]=-0.42+/-0.08, [Si/S]=-0.29+/-0.05, and [Al/S]=-0.53+/-0.08. These ratios
indicate the depletion of Fe, Si, and Al into dust grains, since S is mostly
undepleted. The detection of dust provides an important constraint on the
origin of Complex C, as dust grains indicate the gas has been processed through
galaxies, rather than being purely extragalactic. We also derive a low
metallicity of Complex C of [S/H]=-0.51+/-0.16 (31% solar), confirming earlier
results from this sightline. We discuss origin models that could explain the
presence of dust in Complex C, including Galactic fountain models, tidal
stripping from the Magellanic Clouds or other satellite galaxies, and
precipitation of coronal gas onto dust-bearing ``seed" clouds.
