Using a recently developed approach to constructing covalent network structures from linear carbyne, we identify by ab initio calculations a new carbon allotrope in R3m (D5 3d) symmetry that comprises six-fold helical chains with alternating sp2-type single and double bonds along the chains that are connected via zigzag benzene rings. This 6-fold carbene is characterized as a three-dimensional three-connected chiral crystalline modification of graphite. Phonon and electronic band calculations indicate that this new structure is dynamically stable and is a semiconductor with a band gap of 0.47 eV, in contrast to the semimetallic nature of graphite. Simulated x-ray diffraction patterns of the 6-fold carbene provide an excellent match to the previously unexplained distinct diffraction peak of a new carbon allotrope found in recent detonation experiments. These results establish a new carbon phase and offer insights into its outstanding structural and electronic properties.