We present chemical abundance measurements for seven stars with metallicities ranging from [Fe/H] = $-$3.3 to [Fe/H] = $-$2.4 in the Tucana II ultra-faint dwarf galaxy (UFD), based on high-resolution spectra obtained with the MIKE spectrograph on the 6.5 m Magellan-Clay Telescope. For three stars, we present detailed chemical abundances for the first time. Of those, two stars are newly discovered members of Tucana II and were selected as probable members from deep narrow band photometry of the Tucana II UFD taken with the SkyMapper telescope. This result demonstrates the potential for photometrically identifying members of dwarf galaxy systems based on chemical composition. One new star was selected from the membership catalog of Walker et al. (2016). The other four stars in our sample have been re-analyzed, following additional observations. Overall, six stars have chemical abundances that are characteristic of the UFD stellar population. The seventh star shows chemical abundances that are discrepant from the other Tucana II members and an atypical, higher strontium abundance than what is expected for typical UFD stars. While unlikely, its strontium abundance raises the possibility that it may be a foreground metal-poor halo star with the same systemic velocity as Tucana II. If we were to exclude this star, Tucana II would satisfy the criteria to be a surviving first galaxy. Otherwise, this star implies that Tucana II has likely experienced somewhat extended chemical evolution.
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