  We report on the first study of the noncentrosymmetric ternary carbide
YbCoC$_{2}$. Our magnetization, specific heat, resistivity and neutron
diffraction measurements consistently show that the system behaves as a
heavy-fermion compound, displaying an amplitude-modulated magnetic structure
below the N\'eel temperature reaching $T_{N}$ = 33 K under pressure. Such a
large value, being the highest among the Yb-based systems, is explained in the
light of our ab initio calculations, which show that the 4f electronic states
of Yb have a dual nature -- i.e., due to their strong hybridization with the 3d
states of Co, 4f states expose both localized and itinerant properties.
