We present the first results from a long-term program to measure the t
rigonometric parallaxes and proper motions of a set of pulsars using V
LBI. We obtained these results for PSR B2021+51 from four sessions of
S-band observations of the pulsar and associated reference sources. We
estimate a parallax of 0.95 +/- 0.37 mas, a proper motion of mu(alpha
) = -8.11 +/- 0.24 mas yr(-1) and mu delta = +13.41 +/- 0.25 mas yr(-1
), and a position at epoch 1992.723 of alpha = 20(h)22(m)49(s)87031 +/
- 0.(s)00004 and delta = 51 degrees 54'50.'' 2913 +/- 0.'' 0003 (all J
2000). Our parallax estimate implies an average electron density of 0.
021 +/- 0.008 cm(-3) along the line of sight to the pulsar. We also ef
fectively rule out a physical association with the supernova remnant H
B 21.