  The binary pulsar J2222-0137 is an enigmatic system containing a partially
recycled millisecond pulsar and a companion of unknown nature. Whilst the low
eccentricity of the system favors a white dwarf companion, an unusual double
neutron star system is also a possibility, and optical observations will be
able to distinguish between these possibilities. In order to allow the absolute
luminosity (or upper limit) of the companion object to be properly calibrated,
we undertook astrometric observations with the Very Long Baseline Array to
constrain the system distance via a measurement of annual geometric parallax.
With these observations, we measure the parallax of the J2222-0137 system to be
3.742 +0.013 -0.016 milliarcseconds, yielding a distance of 267.3 +1.2 -0.9 pc,
and measure the transverse velocity to be 57.1 +0.3 -0.2 km/s. Fixing these
parameters in the pulsar timing model made it possible to obtain a measurement
of Shapiro delay and hence the system inclination, which shows that the system
is nearly edge-on (sin i = 0.9985 +/- 0.0005). Furthermore, we were able to
detect the orbital motion of J2222-0137 in our VLBI observations and measure
the longitude of ascending node. The VLBI astrometry yields the most accurate
distance obtained for a radio pulsar to date, and is furthermore the most
accurate parallax for any radio source obtained at "low" radio frequencies
(below ~5 GHz, where the ionosphere dominates the error budget). Using the
astrometric results, we show the companion to J2222-0137 will be easily
detectable in deep optical observations if it is a white dwarf. Finally, we
discuss the implications of this measurement for future ultra-high-precision
astrometry, in particular in support of pulsar timing arrays.
