Single crystals of CeFeAsO, large enough to study the anisotropy of the magnetic properties, were grown by an optimized Sn-flux technique. The high quality of our single crystals is apparent from the highest residual resistivity ratio (RRR)≈12, reported among undoped RFeAsO compounds (R=rare earth) as well as sharp anomalies in resistivity, specific heat, C(T), and thermal expansion at the different phase transitions. The magnetic susceptibility χ(T) presents a large easy-plane anisotropy consistent with the lowest crystal electric field doublet having a dominant Γ₆ character. Curie–Weiss-like susceptibilities for magnetic field parallel and perpendicular to the crystallographic c-axis do not reveal an influence of a staggered field on the Ce site induced by magnetic ordering of the Fe. Furthermore, the standard signatures for antiferromagnetic order of Ce at T_N^4f=3.7 K observed in χ(T) and C(T) are incompatible with a Zeeman splitting Δ≈10 K of the CEF ground state doublet at low temperature due to the Fe-magnetic order as previously proposed. Our results can be reconciled with the earlier observation by assuming a comparatively stronger effect of the Ce–Ce exchange leading to a reduction of this Zeeman splitting below 15 K.