We report on molecular beam epitaxy growth of stoichiometric and superconducting FeSe crystalline thin films
on double-layer graphene. Layer-by-layer growth of high-quality films has been achieved in a well-controlled
manner by using Se-rich condition, which allow us to investigate the thickness-dependent superconductivity
of FeSe. In situ low-temperature scanning tunneling spectra reveal that the local superconducting gap in the
quasiparticle density of states is visible down to two triple layers for the minimum measurement temperature of
2.2 K, and that the transition temperature Tc scales inversely with film thickness.