In his book, Life on a young planet, A.H. Knoll states that the first documented fossils of green algae date back 750 Ma. However, according to B. Teyssèdre's book, La vie invisible, they are much older. Using a method which combines paleontology and molecular phylogeny, this paper is an inquiry into the Precambrian fossils of some "acritarchs" and of a primitive clade of green algae, the Pyramimonadales. A paraphyletic group of unicellular green algae, named "Prasinophyceae", is represented at Thule (Greenland) ca. 1200 Ma by several morphotypes of the monophyletic Pyramimonadales, including Tasmanites and Pterospermella that are akin to algae still living today. These two, and others, probably had forerunners going back 1450 / 1550 Ma. Some acritarchs that may represent Pyramimonadales producing "phycomas" which split open for dehiscence were confusingly included in the polyphyletic pseudo-taxon "Leiosphaeridia" and are possibly already present at Chuanlinggou, China, ca. 1730 Ma. Many acritarchs that Timofeev obtained by acid maceration of Russian samples dated between 1800 and 2000 Ma were probably unicellular Chlorophyta which synthesized algaenans or other biopolymers resistant to acetolysis. Living Prasinophyceae are undoubtedly green algae (Viridiplantae). Thus, if Prasinophyceae fossils go back certainly to 1200 Ma, probably to 1500 Ma and possibly to 1730 Ma, then the ancestor of green algae (Chlorophyta and Streptophyta) probably separated from the ancestor of red algae (Rhodophyta) as early as 2000 Ma.