From John D. Barrow’s chapter in Design and Disorder:
The standard folklore about chaotic systems is that they are unpredictable. They lead to out-of-control dinosaur parks and out-of-work meteorologists. …
Classical … chaotic systems are not in any sense intrinsically random or unpredictable. They merely possess extreme sensitivity to ignorance. Any initial uncertainty in our knowledge of a chaotic system’s state is rapidly amplified in time.
… although they become unpredictable when you try to determine the future from a particular uncertain starting value, there may be a particular stable statistical spread of outcomes after a long time, regardless of how you started out.
Related post: Random is as random does