We examine the rotational dynamics associated with bounded chaotic flows, such as those on chaotic attractors, and find that the dynamics typically exhibits on-off intermittency. In particular, a properly defined chaotic rotation 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 systems, and an argument is provided for the generality of this behavior.