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We use the first systematic samples of CO millimeter emission in z ≥ 1 "main-sequence" star-forming galaxies to study the metallicity dependence of the conversion factor αCO, 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 Ms ~ 101l M⊙. 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 Ms 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(αCO)-log (metallicity) relation to range between -1 and -2, fairly insensitive to the assumed slope of the gas-SFR 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 Ms. [ABSTRACT FROM AUTHOR]