  We find chiral non-Abelian vortices having windings only in one of the
diquark condensations of left-handed and right-handed quarks in the
color-flavor locked phase of dense QCD. They are 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 carry ${\mathbb C}P^2$
orientational moduli in the internal space corresponding to their fluxes. The
${\mathbb C}P^2$ moduli of two chiral non-Abelian vortices with chiralities
opposite to each other are energetically favored to be aligned while those of a
vortex and anti-vortex to be orthogonal, and then these vortices attract each
other. They are attached by chiral domain walls in the presence of the mass and
axial anomaly terms explicitly breaking axial and chiral symmetries. We
numerically show that two chiral non-Abelian vortices with chiralities opposite
to each other are connected by a chiral domain wall, consisting a mesonic bound
state which 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. Furthermore,
we find that chiral non-Abelian 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.
