  We report a new critical solution found at the threshold of axisymmetric
gravitational collapse of a complex scalar field with angular momentum. To
carry angular momentum the scalar field cannot be axisymmetric; however, its
azimuthal dependence is defined so that the resulting stress energy tensor and
spacetime metric are axisymmetric. The critical solution found is
non-spherical, discretely self-similar with an echoing exponent of 0.42 (+-
4%), and exhibits a scaling exponent of 0.11 (+- 10%) in near critical
collapse. Our simulations suggest that the solution is universal (within the
imposed symmetry class), modulo a family-dependent constant phase in the
complex plane.
