  We report the detection of CO(2-1) and 3.1 mm and 1.3 mm continuum emission
towards the extremely young starburst in NGC 5253, with data taken from the
Owens Valley Millimeter Array. Faint CO emission originates in five molecular
clouds distributed along the prominent dust lane seen in visual images. With
the gas, the morphology of NGC 5253 looks much like a dwarf elliptical version
of the ``dust-lane ellipticals'' or ``polar-ring'' class of galaxies. The
molecular gas resides in GMCs well away from the radio-IR super-star
cluster/supernebula seen in the radio and infrared. The millimeter continuum
data confirm that the 2 cm flux from the supernebula is optically thick; the
Lyman continuum rate derived from the 1.3 mm continuum is N$_{Lyc} \sim
6x10^{52} s^{-1}$ for the central ~20''. CO may underestimate the true
molecular column density, as expected for a low metallicity system, although
there are regions along the dust lane that appear to have near-Galactic
conversion factors. We estimate a total molecular gas mass of $M_{H_{2}}\lsim
10^{7} M_{\odot}$. The molecular gas in the dust lane is falling into the
galaxy, supporting an accretion hypothesis. The dust lane gas cannot therefore
be causally associated with the current burst of star formation. A relatively
small amount, $M_{H_{2}}\lsim 5x10^{5} M_{\odot}$, of molecular gas is
associated with the current starburst. We estimate a star formation efficiency
of at least 25 % and more likely ~75 %, consistent with the formation of a
bound cluster. Despite the extreme youth of the starburst, the specific trigger
of the starburst remains elusive, although the infall of gas in the dust lane
suggests that there is more star formation to come in NGC 5253.
