We present a study of the recently discovered compact stellar system Triangulum II. From observations conducted with the DEIMOS spectrograph on Keck II, we obtained spectra for 13 member stars that follow the CMD features of this very faint stellar system and include two bright red giant branch stars. Tri II has a very negative radial velocity (<v_r>=-383.7^{+3.0}_{-3.3} km/s) that translates to <v_{r,gsr}> ~ -264 km/s and confirms it is a Milky Way satellite. We show that, despite the small data set, there is evidence that Tri II has complex internal kinematics. Its radial velocity dispersion increases from 4.4^{+2.8}_{-2.0} km/s in the central 2 to 14.1^{+5.8}_{-4.2} km/s outwards. The velocity dispersion of the full sample is inferred to be sigma_{vr}=9.9^{+3.2}_{-2.2} km/s. From the two bright RGB member stars we measure an average metallicity <[Fe/H]>=-2.6+/-0.2, placing Tri II among the most metal-poor Milky Way dwarf galaxies. In addition, the spectra of the fainter member stars exhibit differences in their line widths that could be the indication of a metallicity dispersion in the system. All these properties paint a complex picture for Tri II, whose nature and current state are largely speculative. The inferred metallicity properties of the system however lead us to favor a scenario in which Tri II is a dwarf galaxy that is either disrupting or embedded in a stellar stream.
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