A small early Tarsiiforme specimen, named Archicebus achilles, lived some 55 million years ago in what is now Central China, it has been known from a recently discovered fossil (right).
This primate was already an ancestor of modern tarsiers, then just diverged from the line leading to us Anthropoidea, what comes to support the theories that suggest an old origin of the primate lineage, possibly c. 85 Ma ago, still in the Cretaceous era, when T. rex and all the famous Hollywood dinosaurs still roamed the Earth.
And this has of course implications as well for the origin of mammals, popularly believed to be in a very early stage of their evolution in that period... but maybe much more diversified than some pop documentaries want us believe.
Until now the oldest known primate was Plesiadapsis, a proto-lemur that may look maybe more like a squirrel than a primate (at least to my eyes). Plesiadapsis is from the same time as Achicebus, c. 55-58 Ma ago.
|Primate phylogenetic tree (from Wikipedia) with the aprox. placement of Archicebus|
Ref. X. Ni et al. The oldest known primate skeleton and early haplorhine evolution. Nature. Vol. 498, June 6, 2013, p. 60. doi:10.1038/nature12200.
Update (Jan 2015): Purgatorius, an even older primate-like mammal, dated to c. 65 Ma ago, was already tree adapted in ways unique to primates (i.e. it was an early primate and not related to rodents anymore in spite of its squirrel-like appearance), new research has found. This is concordant with the placing of Archicebus early in the tarsier branch as shown above.