  The Boomerang Nebula is the coldest known object in the Universe, and an
extreme member of the class of Pre-Planetary Nebulae, objects which represent a
short-lived transitional phase between the AGB and Planetary Nebula
evolutionary stages. Previous single-dish CO (J=1-0) observations (with a 45
arcsec beam) showed that the high-speed outflow in this object has cooled to a
temperature significantly below the temperature of the cosmic background
radiation. Here we report the first observations of the Boomerang with ALMA in
the CO J=2-1 and J=1-0 lines to resolve the structure of this ultra-cold
nebula. We find a central hourglass-shaped nebula surrounded by a patchy, but
roughly round, cold high-velocity outflow. We compare the ALMA data with
visible-light images obtained with HST and confirm that the limb-brightened
bipolar lobes seen in these data represent hollow cavities with dense walls of
molecular gas and dust producing both the molecular-emission-line and
scattered-light structures seen at millimeter and visible wavelengths. The
large diffuse biconical shape of the nebula seen in the visible is likely due
to preferential illumination of the cold high-velocity outflow. We find a
compact source of millimeter-wave continuum in the nebular waist -- these data,
together with sensitive upper limits on the radio continuum using observations
with ATCA, indicate the presence of a substantial mass of very large (mm-sized)
grains in the waist of the nebula. Another unanticipated result is the
detection of CO emission regions beyond the ultracold region which indicate the
re-warming of the cold gas, most likely due to photoelectric grain heating.
