We utilize elemental-abundance information for Galactic red giant stars in five open clusters (NGC 7789, NGC 6819, M67, NGC 188, and NGC 6791) from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) DR13 data set to age-date the chemical evolution of the high- and low-α element sequences of the Milky Way (MW). Key to this time-stamping is the cluster NGC 6791, whose stellar members have mean abundances that place it in the high-α, high-[Fe/H] region of the [α/Fe]–[Fe/H] plane. Based on the cluster’s age (∼8 Gyr), Galactocentric radius, and height above the Galactic plane, as well as comparable chemistry reported for APOGEE stars in Baade’s Window, we suggest that the two most likely origins for NGC 6791 are as an original part of the thick disk, or as a former member of the Galactic bulge. Moreover, because NGC 6791 lies at the high-metallicity end ([Fe/H] ∼ 0.4) of the high-α sequence, the age of NGC 6791 places a limit on the youngest age of stars in the high-metallicity, high-α sequence for the cluster’s parent population (i.e., either the bulge or the disk). In a similar way, we can also use the age and chemistry of NGC 188 to set a limit of ∼7 Gyr on the oldest age of the low-α sequence of the MW. Therefore, NGC 6791 and NGC 188 are potentially a pair of star clusters that bracket both the timing and the duration of an important transition point in the chemical history of the MW.