  We present sensitive CO (J = 1 - 0) emission line observations of three
metal-poor dwarf irregular galaxies Leo P (Z ~ 3% Z_Solar), Sextans A (Z ~ 7.5%
Z_Solar), and Sextans B (Z ~ 7.5% Z_Solar), all obtained with the Combined
Array for Millimeter-wave Astronomy (CARMA) interferometer. While no CO
emission was detected, the proximity of the three systems allows us to place
very stringent (4 sigma) upper limits on the CO luminosity (L_CO) in these
metal-poor galaxies. We find the CO luminosities to be L_CO < 2900 K km/s pc^2
for Leo P, L_CO < 12400 K km/s pc^2 for Sextans A, and L_CO < 9700 K km/s pc^2
for Sextans B. Comparison of our results with recent observational estimates of
the factor for converting between L_CO and the mass of molecular hydrogen, as
well as theoretical models, provides further evidence that either the CO-to-H_2
conversion factor increases sharply as metallicity decreases, or that stars are
forming in these three galaxies very efficiently, requiring little molecular
hydrogen.
