  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.
