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We present time series radial velocity, and photometric observations of a solar-type double-lined eclipsing binary star (V 12) in the old open cluster NGC 188. We use these data to determine the spectroscopic orbit and the photometric elements for V 12. From our analysis, we determine accurate masses (M_p= 1.103±0.007 M_☉, M_s= 1.081±0.007 M_☉) and radii (R_p= 1.424±0.019 R_☉, R_s= 1.373±0.019 R_☉) for the primary (p) and secondary (s) binary components. We adopt a reddening of E_B–V= 0.087 for NGC 188, and derive component effective temperatures of 5900±100 K and 5875±100 K, respectively, for the primary and secondary stars. From their absolute dimensions, the two components of V 12 yield identical distance moduli of V₀- M_V= 11^m.24±0^m.09, corresponding to 1770 ±75 pc. Both stars are near the end of their main-sequence evolutionary phase, and are located at the cluster turnoff in the color-magnitude diagram. We determine an age of 6.2±0.2 Gyr for V 12 and NGC 188, from a comparison with theoretical isochrones in the mass-radius diagram. This age is independent of distance, reddening, and color-temperature transformations. We use isochrones from Victoria-Regina (VRSS) and Yonsei-Yale (Y ²) with [Fe/H] = -0.1 and [Fe/H] = 0.0. From the solar metallicity isochrones, an age of 6.4 Gyr provides the best fit to the binary components for both sets of models. For the isochrones with [Fe/H] = -0.1, ages of 6.0 Gyr and 5.9 Gyr provide the best fits for the (VRSS) and (Y ²) models, respectively. We use the distance and age estimates for V 12, together with best estimates for the metallicity and reddening of NGC 188, to investigate the locations of the corresponding VRSS and Y ² isochrones relative to cluster members in the color-magnitude diagram. Plausible changes in the model metallicity and distance to better match the isochrones to the cluster sequences, result in a range of ages for NGC 188 that is more than 3 times that resulting from our analysis of V 12.