  Using the Very Long Baseline Array, we have made astrometric observations of
the binary pulsar B1913+16 spanning an 18 month period in 2014 - 2015. From
these observations we make the first determination of the annual geometric
parallax of B1913+16, measuring $\pi= 0.24^{+0.06}_{-0.08}$ milliarcseconds
(68% confidence interval). The inferred parallax probability distribution
differs significantly from a Gaussian. Using our parallax measurement and prior
information on the spatial and luminosity distributions of the millisecond
pulsar population, we infer a distance of $d=4.1^{+2.0}_{-0.7}$ kpc, which is
significantly closer than the $9.8 \pm 3.1$ kpc suggested by the pulsar's
dispersion measure and analyses of the ionized interstellar medium. While the
relatively low significance of the parallax detection ($\sim$3$\sigma$)
currently precludes an improved test of general relativity using the orbital
decay of PSR B1913+16, ongoing observations with improved control of systematic
astrometric errors could reach the 10% distance uncertainty required for this
goal. The proper motion measured by our VLBI astrometry differs substantially
from that obtained by pulsar timing, a discrepancy that has also been found
between the proper motion measurements made by interferometers and pulsar
timing for some other pulsars and which we speculate is the result of timing
noise or dispersion measure variations in the timing data set. Our parallax and
proper motion measurements yield a transverse velocityof $15^{+8}_{-4}$ km
s$^{-1}$ in the solar reference frame. Analysis incorporating galactic rotation
and solar motion finds the space velocity of the pulsar relative to its
standard of rest has a component 22$^{+7}_{-3}$ km s$^{-1}$ perpendicular to
the galactic plane and components of order 100 km s$^{-1}$ parallel to the
galactic plane.
