  The A star 49 Ceti, at a distance of 61 pc, is unusual in retaining a
substantial quantity of molecular gas while exhibiting dust properties similar
to those of a debris disk. We present resolved observations of the disk around
49 Ceti from the Submillimeter Array in the J=2-1 rotational transition of CO
with a resolution of 1.0x1.2 arcsec. The observed emission reveals an extended
rotating structure viewed approximately edge-on and clear of detectable CO
emission out to a distance of ~90 AU from the star. No 1.3 millimeter continuum
emission is detected at a 3-sigma sensitivity of 2.1 mJy/beam. Models of disk
structure and chemistry indicate that the inner disk is devoid of molecular
gas, while the outer gas disk between 40 and 200 AU from the star is dominated
by photochemistry from stellar and interstellar radiation. We determine
parameters for a model that reproduces the basic features of the spatially
resolved CO J=2-1 emission, the spectral energy distribution, and the
unresolved CO J=3-2 spectrum. We investigate variations in disk chemistry and
observable properties for a range of structural parameters. 49 Ceti appears to
be a rare example of a system in a late stage of transition between a gas-rich
protoplanetary disk and a tenuous, virtually gas-free debris disk.
