The ground state properties of CeFePO, a homologue of the new high temperature superconductors RFePnO(1-x)Fx, were studied by means of susceptibility, specific heat, resistivity, and NMR measurements on polycrystals. All the results demonstrate that this compound is a magnetically non-ordered heavy Fermion metal with a Kondo temperature TK~10K, a Sommerfeld coefficient gamma=700mJ/molK2 and a mass enhancement factor of the order of 200. The absence of a Fe-contribution to the effective moment at high temperatures indicates that the magnetism in CeFePO is completely dominated by the effect of Ce. Thus the strong electronic correlation effects originate from the Ce-4f electrons rather than from the Fe-3d electrons. An enhanced Sommerfeld-Wilson ratio R=5.5 as well as a Korringa product S0/T1TK2~0.065 well below 1 indicate the presence of ferromagnetic correlations. Therefore, CeFePO appears to be on the non-magnetic side of a ferromagnetic instability.