  The integrated X-ray luminosity ($L_{\mathrm{X}}$) of high-mass X-ray
binaries (HMXBs) in a galaxy is correlated with its star formation rate (SFR),
and the normalization of this correlation increases with redshift. Population
synthesis models suggest that the redshift evolution of $L_{\mathrm{X}}$/SFR is
driven by the metallicity ($Z$) dependence of HMXBs, and the first direct
evidence of this connection was recently presented using galaxies at $z\sim2$.
To confirm this result with more robust measurements and better constrain the
$L_{\mathrm{X}}$-SFR-$Z$ relation, we have studied the $Z$ dependence of
$L_{\mathrm{X}}$/SFR at lower redshifts. Using samples of star-forming galaxies
at $z=0.1-0.9$ with optical spectra from the hCOSMOS and zCOSMOS surveys, we
stacked \textit{Chandra} data from the COSMOS Legacy survey to measure the
average $L_{\mathrm{X}}$/SFR as a function of $Z$ in three redshift ranges:
$z=0.1-0.25$, $0.25-0.4$, and $0.5-0.9$. We find no significant variation of
the $L_{\mathrm{X}}$-SFR-$Z$ relation with redshift. Our results provide
further evidence that the $Z$ dependence of HMXBs is responsible for the
redshift evolution of $L_{\mathrm{X}}$/SFR. Combining all available $z>0$
measurements together, we derive a best-fitting $L_{\mathrm{X}}$-SFR-$Z$
relation and assess how different population synthesis models describe the
data. These results provide the strongest constraints to date on the
$L_{\mathrm{X}}$-SFR-$Z$ relation in the range of $8.0<$12+log(O/H)$<9.0$.
