Structural features of a theory—not merely its limiting behavior—define what phenomena that theory can instantiate, so chaos defined by sensitivity is categorically absent from quantum mechanics.

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Categorically absent(as used in metaphysics and logic): Completely impossible or ruled out by the very nature of something, not just unlikely—it cannot exist within that system at all.
Chaos (in physics)(as used in physics and dynamical systems): A state of disorder where tiny changes in starting conditions lead to completely different outcomes, making systems unpredictable—like how a butterfly's wings might theoretically cause a tornado.
Quantum mechanics(the scientific framework being discussed): The science of how the tiniest things in the universe (atoms, electrons, photons) behave—which turns out to work very differently than everyday objects.
Sensitivity (to initial conditions)(as used in chaos theory): When a system is extremely sensitive to its starting point, so that even microscopic differences at the beginning lead to vastly different results later.

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