Not a primate, but <a href="https://en.wikipedia.org/wiki/Cyclops_%28genus%29">Cyclops</a> is the appropriately named genus that features a single eye.

A single eye birth defect <a href="https://en.wikipedia.org/wiki/Cyclopia">cyclopia</a> found in any number of species, including humans. From evolutionary theory, nothing would prevent such a birth defect from becoming isolated and forming a separate species. This particular birth defect often results in miscarriage and usually associated with a defective nose and results in suffocation. So, this particular form of birth defect is very unlikely to result in a separate breeding population. A different defect that results in a single eye without the other health issues would be more likely to breed effectively.

Even if a trait is a disadvantage, if it breeds true, it can be the basis of a new species. For example, one-eyed are considered unfit mates, so they don't interbreed with the two eyes population. Genetic isolation is essentially the definition of a new species. Further genetic drift would be expected over time.