When organisms die they often leave a black residue of decayed biomolecules--remains that appear indistinguishable from abiotic organic chemicals in carbon-rich meteorites. How might one identify ancient signs of life from such molecular fragments? In the past, paleontologists have looked for specific diagnostic biomolecules, such as those that form cell membranes or gather light in photosynthesis. However, no such markers of life are known to have survived in rocks older than about 1.7 billion years. We have adopted a different strategy, using machine learning to look for subtle patterns in the distribution of all molecular fragments--not just identifiable biomolecules. It turns out that the distributions of life's molecules, which are selected for their biological functions, are quite different from abiotic molecules. Our machine learning method easily teases out biotic from abiotic suites of molecules in rocks as old as 3.33 billion years, while pointing to photosynthetic life in 2.5 billion year old rocks. These methods might also be applied to the search for life on other worlds, even if those lifeforms are different from Earth biology.