  This paper presents maps of the J=2-1 transition of CO toward the Draco
Nebula Intermediate Velocity Cloud (IVC). The maps cover 8500 square arcmin
with a velocity resolution of 0.33 km~s$^{-1}$ and angular resolution of 38",
or 0.11 pc at the cloud distance of 600 pc. The mapped area includes all the
emission detected by the {\it Herschel} satellite with 250 $\mu$m intensity >5
MJy/sr. Previously published observations of the far-IR emission and the 21 cm
line of HI are used to derive the column density distribution of H$_2$ and the
abundance ratio CO/H$_2$, as well as the distribution of the molecular fraction
of hydrogen, which approaches 90\% over much of the brighter parts of the
nebula. The CO emission is highly clumpy and closely resembles the structures
seen in far-IR images. The kinematics of the CO show supersonic motions between
clumps but near-thermal to trans-sonic motions within clumps, consistent with
model predictions that the scale length for dissipation of supersonic
turbulence should be $\sim0.1$ pc, mediated by kinematic viscosity and/or
ambipolar diffusion. Different parts of the nebula show evidence for a spread
of molecular formation timescales of a few 10$^5$ years, comparable to the
dynamical timescale of the infalling gas. The IVC will likely merge with the
Galactic interstellar medium in $\sim 10^7$ years, and the densest clumps may
form an unbound cluster of low-mass stars.
