  We present the first proper motion measurement for an ultra-faint dwarf
spheroidal galaxy, Segue 1, using SDSS and LBC data as the first and second
epochs separated by a baseline of $\sim 10$ years. We obtain a motion of
$\mu_{\alpha}\,\cos(\delta) = -0.37\pm0.57$ mas yr$^{-1}$ and $\mu_{\delta}
=-3.39\pm0.58$ mas yr$^{-1}$. Combining this with the known line-of-sight
velocity, this corresponds to a Galactocentric V$_\mathrm{rad}=84\pm9$ and
V$_\mathrm{tan}=164^{+66}_{-55}$ km s$^{-1}$. Applying Milky Way halo masses
between 0.8 to 1.6$\times 10^{12}$ M$_\odot$ results in an apocenter at
33.9$^{+21.7}_{-7.4}$ kpc and pericenter at 15.4$^{+10.1}_{-9.0}$ kpc from the
Galactic center, indicating Segue~1 is rather tightly bound to the Milky Way.
Since neither the orbital pole of Segue 1 nor its distance to the Milky Way is
similar to the more massive classical dwarfs, it is very unlikely that Segue 1
was once a satellite of a massive known galaxy. Using cosmological zoom-in
simulations of Milky Way-mass galaxies, we identify subhalos on similar orbits
as Segue~1, which imply the following orbital properties: a median first infall
8.1$^{+3.6}_{-4.3}$ Gyrs ago, a median of 4 pericentric passages since then and
a pericenter of 22.8$^{+4.7}_{-4.8}$ kpc. This is slightly larger than the
pericenter derived directly from Segue 1 and Milky Way parameters, because
galaxies with a small pericenter are more likely to be destroyed. Of the
surviving subhalo analogs only 27\% were previously a satellite of a more
massive dwarf galaxy (that is now destroyed), thus Segue 1 is more likely to
have been accreted on its own.
