We report the first comprehensive high-resolution angle-resolved photoemission measurements on CeFeAsO, a parent compound of FeAs-based high temperature superconductors with a magnetic-structural transition at ∼150 K. In the magnetic-ordering state, four holelike Fermi surface sheets are observed near Γ(0,0), and the Fermi surface near M(±π,±π) shows a tiny electronlike pocket at M surrounded by four strong spots. The unusual Fermi surface topology deviates strongly from the band structure calculations. The electronic signature of the magnetic-structural transition shows up in the dramatic change of the quasiparticle scattering rate. A dispersion kink at ∼25 meV is observed for the first time in the parent compound of Fe-based superconductors.