We undertake the first high-resolution spectroscopic study of the Triangulum-Andromeda (TriAnd) star cloud—an extended, mid-latitude Milky Way (MW) halo substructure about 20 kpc away in the second Galactic quadrant— through six M giant star candidates selected to be both spatially and dynamically associated with this system. The abundance patterns of [Ti/Fe], [Y/Fe], and [La/Fe] as a function of [Fe/H] for these stars support TriAnd as having an origin in a dwarf galaxy with a chemical enrichment history somewhat similar to that of the Sagittarius dwarf spheroidal galaxy. We also investigate the previously proposed hypothesis that TriAnd is an outlying, dynamically older piece of the Monoceros Stream (also known as the Galactic Anticenter Stellar Structure, "GASS") under the assumption that both features come from the tidal disruption of the same accreted MW satellite and find that net differences in the above abundance patterns between the TriAnd and GASS stars studied suggest that these two systems are independent and unrelated.