|Monkey-Rocket to Mars!|
The Bion satellite program was a Soviet program (and later a joint U.S.-Soviet program) to investigate the interactions of life science and astronomy. Between December 14, 1983, and January 7, 1997, Bion 6 through 11 used rhesus monkeys as test subjects in unmanned space flights.
Publicly, that is the USSR's only foray into primate research. However, many records have been buried regarding the former USSR. No doubt buried in some old GRU warehouse, there may exist records of a failed test rocket flight from the 1950s. The exact cause of failure is unknown, but the capsule was not recovered, and all primates on board were presumed dead.
It is not clear whether the capsule froze, placing the apes in some sort of cryogenic stasis, or whether the capsule hit a wormhole or was somehow flung at relativistic speeds, but whatever the case, the capsule made its way to Carcosa. At least some of the primates survived.
And now they're crash-landed on Carcosa.
So You Want to Play a Primate in Carcosa?
These rules assume you're using Carcosa with Lamentations of the Flame Princess: Weird Fantasy Role-Playing. If you're not, you'll have to do a little finagling. (Incidentally, if you're using any third edition resources, there are rules for playing orangutans in Dungeon #94.)
If you're playing any large ape (orangutan, gorilla, maybe even a big chimp) you progress as a Dwarf. If you're a smaller monkey (rhesus, spider monkey, whatever), go ahead and progress as a Halfling. You start with no money.
Ability score generation is modified: you roll 3d6 for Constitution and Wisdom, 4d6 for Dexterity and Strength, and 2d6 for Charisma and Intelligence.
As with dwarfs and halflings, your primate starts with a skill at 3 in 6 and progresses as you level up. Unlike dwarfs and halflings, you get two skills, and they're the same whether you're a monkey or an ape: Bushcraft and Climbing. These skills progress at the same rate as Architecture for dwarfs and Bushcraft for Halflings. (As such, they hit 4-in-6 at level 4, 5-in-6 at level 7, and 6-in-6 at level 10.)
The big drawback is that primates can't read or write, and they don't understand Common (they understand some basic commands in Russian). With Referee approval, your Carcosan ape might eventually learn to understand Common, and may even be able to communicate with a rudimentary sign language, but you probably won't start out that way. (Maybe make a Languages check every time you level up; success indicates you've learned to understand Common, while a second success lets you develop a sign language. If your low Intelligence drops you to a 0 in Languages, you can roll two dice and succeed if you roll snake eyes, if your Referee is generous.)
Primates can use tools, and so can use equipment if they can scrounge any. (The Referee is free to impose penalties if s/he thinks the particular tool is outside the realm of typical primate knowledge.)
Finally, primates have an innate slam (or kick, or claw, or bite, or whatever) attack. Apes deal 1d6 with their innate melee attack, whereas monkeys deal 1d4 with theirs.
And there you go. Your Referee can drop your Soviet wreckage in a random Carcosan hex, and you're ready to go. Go play that drunken monkey one shot you never knew you wanted to play.
Update (12-09-2016): Goblinoid Games has released Apes Victorious, an old school RPG that riffs off Planet of the Apes. It includes character classes representing sapient, humanoid monkeys and apes, and so is probably relevant here.