  Circumbinary disks have been hypothesized to exist around a number of binary
post-AGB stars. Although most of the circumbinary disks have been inferred
through the near IR excess, a few of them are strong emitters of molecular
emission. Here we present high angular resolution observations of the emission
of $^{12}$CO and its isotopomer $^{13}$CO J=2--1 line from the circumstellar
envelope around the binary post-AGB star IRAS 08544$-$4431, which is one of the
most prominent members of this class of objects. We find that the envelope is
resolved in our observations and two separate components can be identified: (a)
a central extended and strong component with very narrow linewidth between 2 -
6 \kms; (b) a weak bipolar outflow with expansion velocity up to 8 \kms. The
central compact component possesses low and variable $^{12}$CO/$^{13}$CO J=2--1
line ratio, indicating optically thick emission of the main isotope. We
estimate a molecular gas mass of 0.0047 M$_\odot$ for this component based on
the optically thinner $^{13}$CO J=2--1 line. We discuss the relation of the
molecular envelope and the circumbinary disk inferred from near IR excess and
compare with other known cases where the distribution of molecular gas has been
imaged at high angular resolution.
