  We present results from spectroscopic observations with the Michigan/Magellan
Fiber System (M2FS) of $147$ stellar targets along the line of sight to the
newly-discovered `ultrafaint' stellar systems Tucana 2 (Tuc 2) and Grus 1 (Gru
1). Based on simultaneous estimates of line-of-sight velocity and
stellar-atmospheric parameters, we identify 8 and 7 stars as probable members
of Tuc 2 and and Gru 1, respectively. Our sample for Tuc 2 is sufficient to
resolve an internal velocity dispersion of $8.6_{-2.7}^{+4.4}$ km s$^{-1}$
about a mean of $-129.1_{-3.5}^{+3.5}$ km s$^{-1}$ (solar rest frame), and to
estimate a mean metallicity of [Fe/H]= $-2.23_{-0.12}^{+0.18}$. These results
place Tuc 2 on chemodynamical scaling relations followed by dwarf galaxies,
suggesting a dominant dark matter component with dynamical mass
$2.7_{-1.3}^{+3.1}\times 10^6$ $\mathrm{M}_{\odot}$ enclosed within the central
$\sim 160$ pc, and dynamical mass-to-light ratio $1900_{-900}^{+2200}$
$\mathrm{M}_{\odot}/L_{V,\odot}$. For Gru 1 we estimate a mean velocity of
$-140.5_{-1.6}^{+2.4}$ km s$^{-1}$ and a mean metallicity of
[Fe/H]=$-1.42_{-0.42}^{+0.55}$, but our sample does not resolve Gru 1's
velocity dispersion. The radial coordinates of Tuc 2 and Gru 1 in Galactic
phase space suggest that their orbits are among the most energetic within
distance $\leq 300$ kpc. Moreover, their proximity to each other in this space
arises naturally if both objects are trailing the Large Magellanic Cloud.
