A long time ago in a galaxy far, far from being understood, life began.

The galaxy was the Milky Way. The planet was Earth. And the earliest known evidence of that life -- rare fossils of simple but mysterious organisms that lived 3.5 billion years ago -- went on display yesterday at the Smithsonian's Museum of Natural History.

They are the oldest known fossils of any kind from anywhere, and they represent the oldest known ancestor of all forms of life on Earth, including human beings.

The fossils, which have never before been displayed for the public in this country, are the remains of moundlike aggregates of one-celled organisms, probably bacteria and primitive algae, called stromatolites.

Stromatolites grow today along the shallow waters off Australia, ranging in size from a few inches to a few feet across. It was not until 1977, however, that paleontologists recognized the fossilized specimens from long ago. Those now on display created a sensation among biologists in 1980 when it was found they dated from 3.5 billion years ago.

They are about a thousand times as old as the earliest known fossils of prehuman hominids and 15 times as old as the earliest dinosaurs. They are neither plant nor animal, being three times as old as the simplest of these advanced forms.

The fossils are close to the oldest that scientists can ever hope to discover. The solar system, including Earth, was formed about 4.6 billion years ago and the oldest known rocks on Earth are 3.8 billion years old. Rocks older than that have long since been ground up or melted down by natural processes to form new rock.

It was not until a mere 570 million years ago, the beginning of the Cambrian period, that evolution suddenly exploded to produce such sophisticated forms of life as true worms and other, more familiar forms.

"The difficulty with an exhibit like this -- talking about the origin of life -- is that there's not a whole lot to show," said Kenneth M. Towe, a Smithsonian paleobiologist who was the chief curator in developing the exhibit. "I'm very pleased to get all this stuff."

The exhibit, which includes a number of other fossils representing the evolutionary transition from one-celled forms to multicelled creatures, is "the best Precambrian collection in the world," Towe said.

To the untrained eye, the fossil stromatolites do not look as if they were ever alive. In cross-section they look more like a bizarre rock formation made of many thin, dome-shaped layers of crumbly substance sandwiched between equally thin layers of more conventional looking rock.

It was only their resemblance to modern stromatolites, Towe said, that led paleobiologists to recognize what they were.

Although stromatolites are relatively large, each is actually a colony of countless microscopic one-celled organisms that started as a mat on the bottom of a shallow sea or lagoon. Periodically the mats were covered by fine-grained mineral sediments, perhaps washed over them in storms. Then new living layers formed on top of the sediments. Over many years, repeated covering and reemergence of the microbes formed hard domes several feet high.

"We don't really know for sure how these organisms lived but the fossils convince us that they did," Towe said.

There is intriguing evidence that the stromatolite-forming organisms were capable of a form of photosynthesis, the process by which today's green plants capture solar energy to power their metabolic processes. In a given region, they all lean in the same direction. Modern Australian stromatolites do the same, leaning to aim their flattish tops northward toward the sun.

Although one spotlighted fossil stromatolite forms the centerpiece of the exhibit, equally dramatic is a huge new mural, painted by Peter Sawyer. It depicts a hypothetical scene from the Earth of 3.5 billion years ago, with a volcano erupting on a distant island, and gentle seas lapping a shore in the foreground studded with scores of stromatolites exposed at low tide.

If the stromatolites don't look like living things, there are other fossils in the exhibit that do. Though from a much later time called the Ediacara, they represent another mysterious era in the evolution of life. Rocks bearing the fossils range in age between 570 million and 670 million years.

These fossils tell of an age in which the oceans were dominated by soft-bodied, shell-less forms such as jellyfish. Though jellyfish still live, many of the Ediacaran fossils are unlike anything alive today. Scientists debate whether the creatures were the ancestors of modern forms or died out as evolutionary experiments that failed.

Next to the Ediacaran fossils, including some donated by the Soviet Union, a diorama recreates an ocean floor aprowl with these bizarre organisms.

The exhibit, called "The Earliest Traces of Life", was designed by the museum's Thomas Thill, and occupies the museum's newest permanent exhibition hall, on the first floor next to the dinosaurs. "This is just a small part of the museum," Towe said, "but it represents 85 percent of Earth's history.