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Abstract When particles sediment in a viscous fluid, the character of their trajectories depends sensitively on the particles’ shape. Here we study the sedimentation of U-shaped rigid disks in a regime where inertia can be neglected. We show that, unlike the case of planar disks which settle in a fixed orientation relative to the direction of gravity, U-shaped disks tend to perform a periodic sequence of pitching and rolling motions which cause their centre of mass to sediment along complex trajectories that range from quasi-periodic spirals to helices. Thus, we demonstrate that particles of achiral shape can sediment along chiral paths whose handedness is determined by their initial orientation rather than their geometry. Our analysis provides a framework in which to interpret the motion of sedimenting particles of arbitrary shape.