  Using the Very Long Baseline Array, we have measured a trigonometric parallax
for the micro quasar GRS 1915+105, which contains a black hole and a K-giant
companion. This yields a direct distance estimate of 8.6 (+2.0,-1.6) kpc and a
revised estimate for the mass of the black hole of 12.4 (+2.0,-1.8) Msun. GRS
1915+105 is at about the same distance as some HII regions and water masers
associated with high-mass star formation in the Sagittarius spiral arm of the
Galaxy. The absolute proper motion of GRS 1915+105 is -3.19 +/- 0.03 mas/y and
-6.24 +/- 0.05 mas/y toward the east and north, respectively, which corresponds
to a modest peculiar speed of 22 +/-24 km/s at the parallax distance,
suggesting that the binary did not receive a large velocity kick when the black
hole formed. On one observational epoch, GRS 1915+105 displayed superluminal
motion along the direction of its approaching jet. Considering previous
observations of jet motions, the jet in GRS 1915+105 can be modeled with a jet
inclination to the line of sight of 60 +/- 5 deg and a variable flow speed
between 0.65c and 0.81c, which possibly indicates deceleration of the jet at
distances from the black hole >2000 AU. Finally, using our measurements of
distance and estimates of black hole mass and inclination, we provisionally
confirm our earlier result that the black hole is spinning very rapidly.
