There is considerable evidence that the early climate of Mars was very different from the inhospitable conditions there today. This early climate was characterized by liquid water on the surface and a dense atmosphere composed predominantly of CO2. The duration of these warm initial conditions on the surface of Mars is uncertain, but theoretical models suggest that they could have persisted for hundreds of millions up to a billion years. From studies of the Earth's earliest biosphere we know that by 3.5 Gyr ago, life had originated on Earth and reached a fair degree of biological sophistication. Surface activity and erosion on Earth make it difficult to trace the history of life before the 3.5-Gyr time frame. If Mars did maintain a clement environment for longer than it took for life to originate on Earth, then the question of the origin of life on Mars follows naturally. The fossil evidence of early life on Earth provides clues as to what form fossils on Mars might take. Of particular interest are stromatolites, macroscopic layered structures that result from the anchoring of sediments by microorganisms living in the photic zone. Since over two thirds of the Martian surface is more than 3.5 Gyr old, the possibility exists that Mars may hold the best record of the events that led to the origin of life, even though there may be no life there today.