  There has been much recent work dedicated to exploring secondary correlations
in the mass-metallicity relation, with significant dependence on both the star
formation rate and HI content being demonstrated. Previously, a paucity of
molecular gas data (combined with sample selection bias) hampered the
investigation of any such relation with molecular gas content. In this work, we
assemble a sample of 221 galaxies from a variety of surveys in the redshift
range 0 < z < 2, to explore the connection between molecular gas content and
metallicity. We explore the effect of gas mass on the mass-metallicity
relation, finding that the offset from the relation is negatively correlated
against both molecular and total gas mass. We then employ a principle component
analysis technique to explore secondary dependences in the mass-metallicity
relation, finding that the secondary dependence with gas mass is significantly
stronger than with star formation rate, and as such the underlying `Fundamental
Metallicity Relation' is between stellar mass, metallicity, and gas mass. In
particular, the metallicity dependence on SFR is simply a byproduct of the
dependence on the molecular gas content, via the Schmidt-Kennicutt relation.
Finally, we note that our principle component analysis finds essentially no
connection between gas-phase metallicity and the efficiency of star formation.
