  We present new Gemini Planet Imager observations of the young exoplanet 51
Eridani b which provide further evidence that the companion is physically
associated with 51 Eridani. Combining this new astrometric measurement with
those reported in the literature, we significantly reduce the posterior
probability that 51 Eridani b is an unbound foreground or background T-dwarf in
a chance alignment with 51 Eridani to $2\times10^{-7}$, an order of magnitude
lower than previously reported. If 51 Eridani b is indeed a bound object, then
we have detected orbital motion of the planet between the discovery epoch and
the latest epoch. By implementing a computationally efficient Monte Carlo
technique, preliminary constraints are placed on the orbital parameters of the
system. The current set of astrometric measurements suggest an orbital
semimajor axis of $14^{+7}_{-3}$ AU, corresponding to a period of
$41^{+35}_{-12}$ years (assuming a mass of $1.75$ $M_{\odot}$ for the central
star), and an inclination of $138^{+15}_{-13}$ deg. The remaining orbital
elements are only marginally constrained by the current measurements. These
preliminary values suggest an orbit which does not share the same inclination
as the orbit of the distant M-dwarf binary, GJ 3305, which is a wide physically
bound companion to 51 Eridani.
