  We use 14-year baseline images obtained with the Wide Field Planetary Camera
2 on board the Hubble Space telescope to derive a proper motion for one of the
Milky Way's most distant dwarf spheroidal companions, Leo II, relative to an
extragalactic background reference frame. Astrometric measurements are
performed in the effective point spread function (ePSF) formalism using our own
developed code. An astrometric reference grid is defined using 3,224 stars that
are members of Leo II that are brighter than magnitude 25 in the F814W band. We
identify 17 compact extra-galactic sources, for which we measure a systemic
proper motion relative to this stellar reference grid. We derive a proper
motion [\mu_{\alpha},\mu_{\delta}]=[+104+/-113,-33+/-151] microarcseconds/yr
for Leo II in the heliocentric reference frame. Though marginally detected, the
proper motion yields constraints on the orbit of Leo II. Given a distance of
230 Kpc and a heliocentric radial velocity +79 km/s, and after subtraction of
the solar motion, our measurement indicates a total orbital motion
266.1+/-128.7 km/s in the Galactocentric reference frame, with a radial
component +21.5+/-4.3 km/s and tangential component 265.2+/-129.4 km/s. The
small radial component indicates that Leo II either has a low-eccentricity
orbit, or is currently close to perigalacticon or apogalacticon distance. We
see evidence for systematic errors in the astrometry of the extragalactic
sources which, while close to being point sources, are slightly resolved in the
HST images. We argue that more extensive observations at later epochs will be
necessary to better constrain the proper motion of Leo II. We provide a
detailed catalog of the stellar and extragalactic sources identified in the HST
data which should provide a solid early-epoch reference for future astrometric
measurements.
