  We perform a density-matrix renormalization-group study of strongly
interacting bosons on a three-leg ladder in the presence of a homogeneous flux.
Focusing on one-third filling, we explore the phase diagram in dependence of
the magnetic flux and the inter-leg tunneling strength. We find several phases
including a Meissner phase, vortex liquids, a vortex lattice, as well as a
staggered-current phase. Moreover, there are regions where the chiral current
reverses its direction, both in the Meissner and in the staggered-current
phase. While the reversal in the latter case can be ascribed to spontaneous
breaking of translational invariance, in the first it stems from an effective
flux increase in the rung direction. Interactions are a necessary ingredient to
realize either type of chiral-current reversal.
