Phys.Org has a report on a claim by some scientists that they have found 3.7 Billion year old fossils in Greenland. Scientists find 3.7 billion-year-old fossil, oldest yet
The area where they found the fossils has recently been exposed after the ice melted off due to Global Warming.
The follils are Stromatolites, which are formed by bacteria which form large colonies. While the bacteria do not survive over time the shells of their colonies do.
The age of the fossils suggests that life must have been abundant more than 3.7 Billion years ago, because the bacteria which formed the stromatolites were a relatively advanced life form.
Not every one is ready to accept the report as being accurate. Some feel that there is insufficient evidence that the formations which were found are really stromatolites.