From an AP story by Marcia Dunn headlined “What time is it on the moon? Europe pushing for a lunar time zone”:

With more lunar missions than ever on the horizon, the European Space Agency wants to give the moon its own time zone.

The agency said space organizations around the world are considering how best to keep time on the moon. The idea came up during a meeting in the Netherlands late last year, with participants agreeing on the urgent need to establish “a common lunar reference time,” said the space agency’s Pietro Giordano, a navigation system engineer.