Not sure how you're defining "organic", but much of the moon is convered with basalt rock like the kind found on earth, and evidently it can be dated. Good question though; I'm open to any different interpretations....
For reference:
Quote:
ba-salt
n.
A hard, dense, dark volcanic rock composed chiefly of plagioclase, pyroxene, and olivine, and often having a glassy appearance.
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Anything in that description fit your definition of "organic"? Maybe they were dated, just not with Carbon-14? Possible I misinterpretted something I read.