  We investigate the sedimentation of chiral particles in viscous fluid flow.
We identify helical ribbons as simple particles with strong
translation-rotation coupling whose symmetry ensures that the centers of mass,
buoyancy, resistance, and mobility coincide. Experimental measurements of both
relevant mobility tensors show excellent agreement with simulations of ribbons
made of interacting spheres. We observe quasi-periodic angular dynamics causing
complex spatial trajectories. In tilt-spin phase space, orbits are closed due
to time-reversal and reflection symmetry. Changing the helical ribbon length
reveals a bifurcation at which the stable sedimentation orientations switch.
