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We report the discovery of a candidate binary system consisting of a black hole (BH) and a red giant branch star from the Gaia DR3. This binary system is discovered from 64108 binary solutions for which both astrometric and spectroscopic data are available. For this system, the astrometric and spectroscopic solutions are consistent with each other, making this system a confident candidate of a BH binary. The primary (visible) star in this system, Gaia DR3 5870569352746779008, is a red giant branch whose mass is quite uncertain. Fortunately, albeit the uncertainty of the primary's mass, we can estimate the mass of the secondary (dark) object in this system to be $>5.68$ $M_\odot$ with a probability of $99$ \%, based on the orbital parameters. The mass of the secondary object is much larger than the maximum neutron star mass ($\sim 2.0$ $M_\odot$), which indicates that the secondary object is likely a BH. We argue that, if this dark object is not a BH, this system must be a more exotic system, in which the primary red giant branch star orbits around a quadruple star system (or a higher-order multiple star system) whose total mass is more than $5.68$ $M_\odot$. If this is a genuine BH binary, this has the longest period ($1352.22 \pm 45.81$ days) among discovered so far. As our conclusion entirely relies on the Gaia DR3 data, independent confirmation with follow-up observations (e.g. long-term spectra) is desired.