We have studied density-dependent time-resolved photoluminescence from a 80 A InGaAs/GaAs single quantum well excited by picosecond pulses. We succeed in giving evidence for the transition from an exciton-dominated population to an unbound electron-hole pair population as the pair density increases. For pair densities below this excitonic Mott transition we observe a spectrally separate emission from free electron-hole pairs in addition to excitonic luminescence, thereby proving the coexistence of both species. Exciton binding energy and band gap remain unchanged even near the upper bound of this coexistence region. Above the Mott density we observe a purely exponential high energy tail of the photoluminescence and a redshift of the band gap with pair density. The transition occurs gradually between 1 x 10(10) and 1 x 10(11) cm(-2) at the carrier temperatures of our experiment.