Chaotic behaviour is found for sufficiently long triaxial ellipsoidal
non-Brownian particles immersed in steady simple shear flow of a Newto
nian fluid in an inertialess approximation. The result is first determ
ined via numerical simulations. An analytic theory explaining the onse
t of chaotic rotation is then proposed. The chaotic rotation coexists
with periodic and quasi-periodic motions. Quasi-periodic motions are d
epicted by regular closed loops and islands in the system Poincare map
, whereas chaotic rotations form a stochastic layer.