The understanding of the nature of intermediate- and high-velocity gas in t
he Milky Way is hampered by a paucity of distance estimates to individual c
louds. A project has been started at the David Dunlap Observatory to addres
s this lack of distance measures by observing early-type stars along the li
ne of sight toward these clouds and searching for sodium doublet absorption
at the clouds' systemic velocities. Distances to foreground stars (no abso
rption) and background stars (with absorption) are estimated from spectrosc
opic parallax, and thus the distance to the bracketed cloud is estimated. I
n this Letter, we present the first result from this ongoing project: a mea
surement of the distance to the Draco Cloud, which is the most studied of t
he intermediate-velocity clouds. The result presented here is the first dis
tance bracket that tightly constrains the position of the Draco Cloud. We b
riefly describe our target selection and observing methodology and then dem
onstrate absorption at the velocity of the Draco Cloud for one star (TYC 41
94 2188) and a lack of absorption for several other stars. We derive a dist
ance bracket to the Draco Cloud of 463(-136)(+192) to 618(-174)(+243) pc.