Look for RNA-World Rock Strata on the Moon

Schulze-Makuch and Crawford show in Astrobiology that that the Moon may have briefly been habitable - either (two options) about 4.5 billion years ago, or 3.5 billion years ago, for a few tens of millions of years, with an atmosphere and some liquid water (Gizmodo digest here.) Since the moon was formed after an impact with the early Earth, we should assume they had many of the same starting materials. The moon had less surface area and less time, and split from the Earth prior to even the earliest suggested prebiotic activity around 4 billion years ago, so it would have had to develop its own life - it could not have been "seeded."

The Moon with life (although terraformed.) From Techeblog.
Recent work by Tashiro et al suggest that a 4 billion year old rock stratum on Earth shows evidence of biological activity and may even be the fossil result of an RNA-World stage in the evolution of life on Earth. If it existed on Earth, it also could have existed on the Moon. It's not as though that rock stratum is exposed everywhere on Earth (the Tashiro people used samples from northern Labrador, Canada.) But it's interesting to think that the same stratum could have existed on the Moon if prebiotic chemistry took a similar course - and that those strata may be much easier to find and more widespread given the inactivity of the Moon relative to Earth.