Rocks from western Australia called the
Warrawoona Group show fossilized prokaryotes:
http://earth.usc.edu/~geol150/evolution/precambrianfossils.html
These rocks are 3.5 billion years old!
More extreme -- but less convincing -- is an
argument that the isotopic makeup of the
Isua (Greenland) metamorphosed sedimentary
rocks indicates that living organisms had to
be present when those sediments were deposited ...
around 3.85 billion years ago!