  We use the first systematic samples of CO millimeter emission in z>1
'main-sequence' star forming galaxies (SFGs) to study the metallicity
dependence of the conversion factor {\alpha}CO, from CO line luminosity to
molecular gas mass. The molecular gas depletion rate inferred from the ratio of
the star formation rate (SFR) to CO luminosity, is ~1 Gyr-1 for near-solar
metallicity galaxies with stellar masses above M_S~1e11 M_sun. In this regime
the depletion rate does not vary more than a factor of two to three as a
function of molecular gas surface density, or redshift between z~0 and 2. Below
M_S the depletion rate increases rapidly with decreasing metallicity. We argue
that this trend is not caused by starburst events, by changes in the physical
parameters of the molecular clouds, or by the impact of the fundamental
metallicity-SFR-stellar mass relation. A more probable explanation is that the
conversion factor is metallicity dependent and that star formation can occur in
'CO-dark' gas. The trend is also expected theoretically from the effect of
enhanced photodissociation of CO by ultraviolet radiation at low metallicity.
From the available z~0 and z~1-3 samples we constrain the slope of the
log({\alpha}CO) -log (metallicity) relation to range between -1 and -2, fairly
insensitive to the assumed slope of the gas-star formation rate relation.
Because of the lower metallicities near the peak of the galaxy formation
activity at z~1-2 compared to z~0, we suggest that molecular gas masses
estimated from CO luminosities have to be substantially corrected upward for
galaxies below M_S.
