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Black hole-main sequence star (BH-MS) binaries are one of the targets of thefuture data releases of the astrometric satellite {\it Gaia}. They are supposedto be formed in two main sites: a galactic field and star clusters. However,previous work has never predicted the number of BH-MS binaries originating inthe latter site. In this paper, we estimate the number of BH-MS binaries formedin open clusters and detectable with {\it Gaia} based on the results of {\itN}-body simulations. By considering interstellar extinction in the Milky Way(MW) and observational constraints, we predict $\sim 10$ BH-MS binaries areobservable. We also find that chemical abundance patterns of companion MSs willhelp us to identify the origin of the binaries as star clusters. Such MSs arenot polluted by outflows of the BH progenitors, such as stellar winds andsupernova ejecta. Chemical anomalies might be a good test to confirm the originof binaries with relatively less massive MSs ($\lesssim 5M_{\odot}$), orbitalperiods ($\sim 1.5\;$year) and higher eccentricities ($e \gtrsim 0.1$).

Gaia's Detectability of Black Hole-Main Sequence Star Binaries Formed in Open Clusters