  The pulsar/massive star binary system PSR B1259-63 / LS 2883 is one of the
best-studied gamma-ray binaries, a class of systems whose bright gamma-ray
flaring can provide important insights into high-energy physics. Using the
Australian Long Baseline Array we have conducted very long baseline
interferometric observations of PSR B1259-63 over 4.4 years, fully sampling the
3.4-year orbital period. From our measured parallax of $0.38\pm0.05$ mas we use
a Bayesian approach to infer a distance of $2.6^{+0.4}_{-0.3}$ kpc. We find
that the binary orbit is viewed at an angle of $154\pm3$ degrees to the line of
sight, implying that the pulsar moves clockwise around its orbit as viewed on
the sky. Taking our findings together with previous results from pulsar timing
observations, all seven orbital elements for the system are now fully
determined. We use our measurement of the inclination angle to constrain the
mass of the stellar companion to lie in the range 15-31$M_{\odot}$. Our
measured distance and proper motion are consistent with the system having
originated in the Cen OB1 association and receiving a modest natal kick,
causing it to have moved $\sim$8 pc from its birthplace over the past
$\sim3\times10^5$ years. The orientation of the orbit on the plane of the sky
matches the direction of motion of the X-ray synchrotron-emitting knot observed
by the Chandra X-ray Observatory to be moving away from the system.
