Fermi surface topology and pairing symmetry are two pivotal characteristics of a superconductor. Superconductivity in one monolayer (1ML) FeSe thin film has attracted great interest recently due to its intriguing interfacial properties and possibly high superconducting transition temperature (Tc) over 77 K. Here, we report high-resolution measurements of the Fermi surface and superconducting gaps in 1ML FeSe using angle-resolved photoemission spectroscopy (ARPES). Two ellipse-like electron pockets are clearly resolved overlapping with each other at the Brillouin zone corner. The superconducting gap is nodeless but moderately anisotropic, which put strong constraints on determining the pairing symmetry. The gap maxima locate along the major axis of ellipse, which cannot be explained by a single d-wave, extended s-wave, or s$pm$ gap function. Four gap minima are observed at the intersection of electron pockets suggesting the existence of either a sign change or orbital-dependent pairing in 1ML FeSe.
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