An attempt has been made to calculate the ages of lunar fines and carbonaceous chondrites from the contents of ^"Pu fission xenon and uranium. The carbonaceous chondrites such as Renazzo and Allende appear to be the oldest objects in the solar system and they began to retain their xenon about 4,900 million years ago when the ratio of 244 Pu to 238 U in the solar system was about 0.123 (atom/atom). Lunar fines, which appear to be the second oldest objects in the solar system, began to retain their xenon 4,568 to 4,857 million years ago, when the ratio of 244 Pu to 238 U was 0.0078 to 0.0855 (atom/atom).