U-Pb systematics were determined from fifteen phosphate separates from equilibrated ordinary chondrites and from small bulk fragments of the same meteorites. The high U-238/Pb-204 ratios of thirteen of these phosphate separates lead to extremely radiogenic Pb whose Pb-206/Pb-204 ratios range from 250 up to 3500. The Pb/Pb model ages for these phosphates range from 4.563 to 4.502 Ga, with an analytical precision of 10(6) y and the U-Pb system is apparently concordant. The time interval observed, 60 x 10(6) y, reflects the thermal processing of the equilibrated chondrites and is consistent with that previously derived from the Rb/Sr, K/Ar and Pu chronologies. The Pb/Pb ages of the phosphates from the seven H chondrites show a negative correlation versus their metamorphic grade. This is the first clear relationship ever observed between a long-lived chronometer and the intensity of metamorphism as reflected by metamorphic grade. Assuming that the Pb/Pb age indicates the accurate U-Pb closure time in phosphates, the Pb/Pb chronology is compatible with the model of a layered H chondrite parent body. However, this interpretation of the U/Pb systematics is not unique; it postulates a slow cooling of the equilibrated materials at high temperature, in apparent conflict with petrological observations. Except for the H chondrites, which agree rather well with Pu systematics, comparison of the Pb/Pb chronology with published radiochronometric data does not reveal simple correlations. In the present debate concerning the thermal history of chondrites, the chronometric information derived from each isotope system is interpreted as the time of its thermal closure. However, this basic assumption may not be correct for all the radiochronologies and must be evaluated before the radiochronometric data can be applied as compelling time constraints for the period of 4.56-4.4 Ga of proto-planetary history.