We present a new Kondo-lattice system, YbNi 4 P 2 , which is a clean heavy-fermion metal with a severely reduced ferromagnetic ordering temperature at T C = 0.17 K, evidenced by distinct anomalies in susceptibility, specific-heat, and resistivity measurements. The ferromagnetic nature of the transition, with only a small ordered moment of ∼ 0.05 µ B , is established by a diverging susceptibility at T C with huge absolute values in the ferromagnetically ordered state, severely reduced by small magnetic fields. Furthermore, YbNi 4 P 2 is a stoichiometric system with a quasi-one-dimensional crystal and electronic structure and strong correlation effects which dominate the low temperature properties. This is reflected by a stronger-thanlogarithmically diverging Sommerfeld coefficient and a linear-in-T resistivity above T C which cannot be explained by any current theoretical predictions. These exciting characteristics are unique among all correlated electron systems and makes this an interesting material for further in-depth investigations. arXiv:1108.4274v1 [cond-mat.str-el]