In a sci-fi setting, could apes really speak? (some spoilers for the Planet of the Apes franchise, mostly "Rise of the Planet of the Apes")

I was recently very moved by the movie "Rise of the Planet of the Apes." What I connected with was the way the movie addressed the cruelty towards other species that a lot of the members of ours considers a matter of course, but the inquisitive/scientific aspect of me also noticed some ideas in the movie that I was not sure were really realistic. So my question is: in a sci-fi world like in the movie, could apes (e.g. chimpanzees) really vocalize human speech? And let me explain: in the movie, the apes' cognitive ability grows beyond most humans'. They display incredible levels of motor control and, arguably, somatic awareness (being able to do things with their body, e.g. do "acrobatics," I think being more agile than realistic "unmodified" apes). They also understand speech at a very high level (and most are capable of language production by means of ASL). Also, this is not a question about reality, but about a thought experiment in a science fiction, not fantasy sense; in SF, the premise is based on real science that is extrapolated in a way that bold (but still logically traceable) hypothesis is fact. E.g. when humans levitate, it's fantasy, but when all humans gain eidetic memory due to exposure to a virus that changes brain chemistry, it's science fiction. We hear very little speech in "Rise...," it's not like the original Planet of the Apes franchise, where the apes have conversations. The few phrases we do hear are unclear but completely intelligible. If you know something about ape (mostly chimpanzee) physiology, and have seen the movie, how possible do you think it is as a science fiction (not fantasy) idea, bearing in mind the advanced IQ and (possible) unnaturally acute somatic (bodily) self-awareness in the apes in the movie? Let's let our minds wonder (in a controlled, science-fiction manner ;)). I will have many discussions about this with other sci-fi fans in the future, so I want to come prepared :)