  We report the emergence of superconductivity in Ca2InN consisting of a
2-dimensional (2D) array of zigzag indium chains embedded between Ca2N layers.
A sudden drop of resistivity and a specific-heat (Cp) jump attributed to the
superconducting transition were observed at 0.6 K. The Sommerfeld coefficient
{\gamma}= 4.24 mJ/mol K2 and Debye temperature {\Theta}D = 322 K were
determined from the Cp of the normal conducting state and the superconducting
volume fraction was estimated to be ~80% from the Cp jump, assuming a BCS-type
weak coupling. Density functional theory calculations demonstrated that the
electronic bands near the Fermi level (EF) are mainly derived from In 5p
orbitals with {\pi} and {\sigma} bonding states and the Fermi surface is
composed of cylindrical parts, corresponding to the quasi-2D electronic state
of the In chain array. By integrating the projected density of states of In-p
component up to EF, a valence electron population of ~1.6 electrons/In was
calculated, indicating that the partially anionic state of In. The In 3d
binding energies observed in Ca2InN by x-ray photoemission spectroscopy were
negatively shifted from that in In metal. The superconductivity of Ca2InN is
associated with the p-p bonding states of the anionic In layer.
