Success in isolating a 2D graphene sheet from bulky graphite has triggered intensive studies of its physical properties as well as its application in devices. Graphite intercalation compounds (GICs) have provided a platform of exotic quantum phenomena such as superconductivity, but it is unclear whether such intercalation is feasible in the thinnest 2D limit (i.e., bilayer graphene). Here we report a unique experimental realization of 2D GIC, by fabricating calcium-intercalated bilayer graphene C(6)CaC(6) on silicon carbide. We have investigated the structure and electronic states by scanning tunneling microscopy and angle-resolved photoemission spectroscopy. We observed a free-electron-like interlayer band at the Brillouin-zone center, which is thought to be responsible for the superconductivity in 3D GICs, in addition to a large π* Fermi surface at the zone boundary. The present success in fabricating Ca-intercalated bilayer graphene would open a promising route to search for other 2D superconductors as well as to explore its application in devices.