There have been several experiments with primates and sign language. All of them have been severely criticized for various reasons.
n.b.- all of the following info is from a linguistics course that I just took.
One of the first attempts at getting a primate to produce human language was actually involving a chimp- they tried to make the chimp say simple words in the hopes of teaching him language. The problem with this is that primates aren’t built for speech as we know it; their articulators (i.e., the basic shape of their mouth) are too different from humans. The chimp was eventually able to make three or four words that were recognizable… if you gave it the benefit of the doubt.
Most attempts at communication afterwards were then contained to sign language.
A better known project involved a chimp who was taken in to the household of a husband and wife science team, the Gardners. They tried to teach it sign language. The Gardners had many assistants and took a lot of video footage, which you might be able to find with a bit of digging. One of the problems with this chimp is that there were questions raised as to what exactly a sign was- that is, the chimp would move it’s hands in a way vaugely approaching a sign, and would then get what it wanted. Linguistics who have reviewed their work say that there is no conclusive data to be drawn.
Another chimp project involved putting a chimp in a cage with a computer. The computer was similar to a device used by some who are incapable of speech- that is, it had buttons with pictures on them. The chimp would press the buttons and, if done in the correct order, it would get the desired result- be it food or what have you. This one was criticized for the artificial construct. There were only certain ways that the chimp could arrange the buttons, so there was no variation for freedom in language.
Koko… well, what everybody else said.
The basic problem with primates and language is that they simply do not mimic the human response to learning language. A child learning a language will increase their vocabulary exponentially, while primates plateau quickly. Primates also don’t do many of the things that have been suggested to be innate in human language- free variation, expiramentation, knowledge of how to structure things.
Lissa is right about the sign teaching chains- if left to their own devices, primates will not spread sign language. It’s just not in their nature, I suppose.