Quaternary convergence at rates of ~10 mm/yr between the Arabian and Eurasian plates is largely accommodated by the Kura fold-thrust belt at the longitude of the Greater Caucasus Mountains in Azerbaijan and eastern Georgia. Here we present the results of the first paleoseismic study of the Kura fold-thrust belt in Azerbaijan. A single paleoseismic trench was excavated across a 2-m-high fault scarp near Agsu revealing evidence of two recent surface rupturing earthquakes. Radiocarbon dating of the faulted sediments places limits of earthquake timing of AD 1713-1895 and AD 1872-2003 for the two events. Allowing for uncertainties in radiocarbon dating, the two events likely correspond to historical destructive M~7 earthquakes near Shamakhi, Azerbaijan in AD 1668 and 1902. Holocene shortening and dip-slip rates for the Kura fold-thrust belt are 8 and 8.5 mm/yr, respectively, based on the depositional age of an abandoned uplifted strath terrace in a water gap to the west of Agsu. These rates should be treated as maxima, as they are ~100% of the previously determined structurally and geodetically measured shortening across the belt, and were measured from only one of two primary structures in this part of the belt. The lack of reported historical ruptures from the past 8 centuries to the west of Agsu, in contrast with the numerous recorded destructive earthquakes of the Shamakhi region, suggests that the central and western parts of the Kura fold-thrust belt produce less frequent, but more destructive earthquakes, and may have accumulated sufficient strain to produce a M>8 earthquake.