  We find chiral non-Abelian semi-superfluid vortices in the color-flavor
locked (CFL) phase of dense QCD as the minimum vortices carrying half color
magnetic fluxes of those of non-Abelian semi-superfluid vortices (color
magnetic flux tubes) and 1/6 quantized superfluid circulations of Abelian
superfluid vortices. These vortices exhibit unique features: one is the
so-called topological obstruction implying that unbroken symmetry generators in
the bulk are not defined globally around the vortices, and the other is color
non-singlet Aharonov-Bohm (AB) phases implying that quarks encircling these
vortices can detect the colors of magnetic fluxes of them at infinite
distances. They are confined by chiral domain walls in the presence of the mass
and axial anomaly terms explicitly breaking axial and chiral symmetries while
they are deconfined in the absence of those terms. In the confined phase, two
chiral non-Abelian semi-superfluid vortices with chiralities opposite to each
other are connected by a chiral domain wall, consisting a mesonic bound state
exhibiting only color singlet AB phases so that the quarks cannot detect the
color of magnetic flux of such a bound state at infinite distances, and the
final state of the mesonic bound state is nothing but a non-Abelian
semi-superfluid vortex. We also show that Abelian and non-Abelian axial
vortices attached by chiral domain walls are all unstable to decay into a set
of chiral non-Abelian vortices.
