What is the lineage relation among the cells of an organism? The answer is sought by developmental biology, immunology, stem cell research, brain research, and cancer research, yet complete cell lineage trees have been reconstructed only for simple organisms such as Caenorhabditis elegans. We discovered that somatic mutations accumulated during normal development of a higher organism implicitly encode its entire cell lineage tree with very high precision. Our mathematical analysis of known mutation rates in microsatellites (MSs) shows that the entire cell lineage tree of a human embryo, or a mouse, in which no cell is a descendent of more than 40 divisions, can be reconstructed from information on somatic MS mutations alone with no errors, with probability greater than 99.95%. Analyzing all approximately 1.5 million MSs of each cell of an organism may not be practical at present, but we also show that in a genetically unstable organism, analyzing only a few hundred MSs may suffice to reconstruct portions of its cell lineage tree. We demonstrate the utility of the approach by reconstructing cell lineage trees from DNA samples of a human cell line displaying MS instability. Our discovery and its associated procedure, which we have automated, may point the way to a future "Human Cell Lineage Project" that would aim to resolve fundamental open questions in biology and medicine by reconstructing ever larger portions of the human cell lineage tree.