We examine the rotational dynamics associated with bounded chaotic flows, s
uch as those on chaotic attractors, and find that the dynamics typically ex
hibits on-off intermittency. In particular, a properly defined chaotic rota
tion tends to follow, approximately, the phase-space rotation of a harmonic
oscillator with occasional bursts away from this nearly uniform rotation.
The intermittent behavior is identified in several well studied chaotic sys
tems, and an argument is provided for the generality of this behavior.