  The understanding of the nature of intermediate and high velocity gas in the
Milky Way is hampered by a paucity of distance estimates to individual clouds.
A project has been started at the David Dunlap Observatory to address this lack
of distance measures by observing early-type stars along the line of sight
towards these clouds and searching for sodium doublet absorption at the clouds'
systemic velocities. Distances to foreground stars (no absorption) and
background stars (with absorption) are estimated from spectroscopic parallax,
and thus the distance to the bracketed cloud is estimated. In this Letter, we
present the first result from this ongoing project, a measurement of the
distance to the Draco Cloud, which is the most studied of the intermediate
velocity clouds. The result presented here is the first distance bracket which
tightly constrains the position of the Draco Cloud. We briefly describe our
target selection and observing methodology, and then demonstrate absorption at
the velocity of the Draco Cloud for one star (TYC~4194~2188), and a lack of
absorption for several other stars. We derive a distance bracket to the Draco
Cloud of 463$^{+192}_{-136}$ to 618$^{+243}_{-174}$~pc.
