There have several attempts to explore to what extent apes can learn language. It has been fundamental part of nature and nurture debate in language acquisition. If they can acquire language it means language acquisition is due to nurture if they can not then it is unique to human being. However, the problem is about what can be contrued as language and what is a simple communication. There is absolutely no doubt what so ever that apes can communicate with human following commands and reacting to stimulus. The issue of language is more complicated.
There has been study by Gardner and Gardner who was able to teach the chimp named "washoe" some words and basic phrases using american sign language. On the other hand Sue Savage Rumbaugh was able to show that her banebo monkeys Kanzi and Mulliaka were able to use lexigram quite efficiently.
A good summary of major researches can be found in this paper