  It is known that nuclear deformation plays an important role in inducing the
halo structure in neutron-rich nuclei by mixing several angular momentum
components. While previous theoretical studies on this problem in the
literature assume axially symmetric deformation, we here consider non-axially
symmetric deformations. With triaxial deformation, the $\Omega$ quantum number
is admixed in a single-particle wave function, where $\Omega$ is the projection
of the single-particle angular momentum on the symmetric axis, and the halo
structure may arise even when it is absent with the axially symmetric
deformation. We apply this consideration to a one-neutron halo nucleus $^{19}$C
and show that the radius and the one-neutron separation energy can be
simultaneously accounted for by taking into account the triaxiality in the
deformation of $^{19}$C.
