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.
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