We present a chemodynamical analysis of the Leo V dwarf galaxy , based on Keck II DEIMOS spectra of 8 member stars . We find a systemic velocity for the system of \langle v _ { r } \rangle = 170.9 ^ { +2.1 } _ { -1.9 } { km s ^ { -1 } } , and barely resolve a velocity dispersion for the system , with \sigma _ { vr } = 2.3 ^ { +3.2 } _ { -1.6 } { km s ^ { -1 } } , consistent with previous studies of Leo V. The poorly resolved dispersion means we are unable to adequately constrain the dark matter content of Leo V. We find an average metallicity for the dwarf of [ Fe/H ] = -2.48 \pm 0.21 , and measure a significant spread in the iron abundance of its member stars , with -3.1 \leq [ Fe/H ] \leq - 1.9 dex , which cleanly identifies Leo V as a dwarf galaxy that has been able to self-enrich its stellar population through extended star formation . Owing to the tentative photometric evidence for tidal substructure around Leo V , we also investigate whether there is any evidence for tidal stripping or shocking of the system within its dynamics . We measure a significant velocity gradient across the system , of \frac { { d } v } { { d } \chi } = -4.1 ^ { +2.8 } _ { -2.6 } { km s ^ { -1 } } per arcmin ( or \frac { { d } v } { { d } \chi } = -71.9 ^ { +50.8 } _ { -45.6 } { km s ^ { -1 } } kpc ^ { -1 } ) , which points almost directly toward the Galactic centre . We argue that Leo V is likely a dwarf on the brink of dissolution , having just barely survived a past encounter with the centre of the Milky Way .