The lunar Mg-suite magmatic rocks are commonly thought to represent mafic intrusions into the anorthositic flotation crust of the lunar magma ocean (LMO). Their geochronology is, therefore, important for constraining evolution models of the LMO. Petrogenetic models of the Mg-suite hold that their parent magmas were derived from primary LMO sources (Mg-cumulates, An-rich plagioclase, and melts enriched in KREEP—potassium, rare earth elements, and phosphorus). Previous radiogenic isotopic age interpretations of Mg-suite and putatively older, related ferroan anorthosites (FANs) overlap over a 200-million-year interval. The Apollo 78238 norite is an exemplary Mg-suite rock, with a relict coarse igneous texture modified by shock metamorphism. In-situ secondary ion mass spectrometry U-Pb analyses of zircon and baddeleyite in 78238 yield discordant arrays, attributed to recent impact metamorphism, with upper intercepts that constrain its crystallization age. The four oldest baddeleyite analyses give a weighted mean 207Pb/206Pb age of 4332 ± 18 Ma (2σ, MSWD = 0.06, P = 0.98), which is interpreted as the crystallization age of the norite. The overlap of the baddeleyite age with previously reported Sm-Nd and Pb-Pb mineral isochron ages for 78238 (Edmunson et al., 2009) supports a moderately fast cooling of the norite. Moreover, it is distinguishably younger than the most precisely dated sample of FAN (Apollo 60025), measured at 4360 ± 3 Ma by Sm-Nd and Pb-Pb mineral isochrons (Borg et al., 2011). Together with the baddeleyite 207Pb/206Pb age of Apollo Mg-suite troctolite 76535 at 4328 ± 8 Ma (White et al., 2020), the chronological record of the 78238 norite indicates a significant Mg-suite magmatic event at 4.33 Ga and a lower age limit on LMO differentiation.