The saturation remanence normalization method of paleointensity estimation has been applied to more than 50 lunar samples, and has been calibrated in terms of standard intensity determinations done on 14 samples. These results suggest that a lunar surface field, comparable in intensity to the earth's magnetic field, existed from about 3.6 to 3.8 AE. Absolute paleointensity estimates and lunar surface field strength determinations are consistent with this observation. The data presented here differ from previous descriptions of the variation in the lunar field with time in that (A) the oldest samples (>3.9 AE) are among the most weakly magnetized; and (B) an order of magnitude drop in paleointensity is suggested between the time of extrusion of the Apollo 11 low and high potassium basalts. The limited range in age of the strongly magnetized lunar samples and the absence of shocked samples in this set argues against a solar source for the lunar paleofield or for fields arising from transient phenomena such as impacts. The coincidence of this high field era with the termination of basin forming impacts and the beginning of mare basalt extrusion suggests a common cause. A close approach of the moon to the earth at about 3.8 AE might account for all three phenomena. The confined duration of the strong lunar field may allow for the assignment of relative ages for certain lunar samples and surface features.