We report the first comprehensive high-resolution angle-resolved photoemission measurements on CeFeAsO, a parent compound of FeAs-based high temperature superconductors with a mangetic/structural transition at $sim$150 K. In the magnetic ordering state, four hole-like Fermi surface sheets are observed near $Gamma$(0,0) and the Fermi surface near M(+/-$pi$,+/-$pi$) shows a tiny electron-like pocket at M surrounded by four Dirac cone-like 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 $sim$ 25meV is for the first time observed in the parent compound of Fe-based superconductors.
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