The first part of this work is dedicated to an experimental investigation of the C-Hf-O system and in particular to the stability domain of the HfCxOy oxycarbide phase formed through the carbothermal reduction in HfO2 by carbon black at 1650 and 1750 degrees C. This study which has been carried out by coupling chemical elemental analysis of powder with a structural approach by X-ray powder diffraction and Transmission Electron Microscopy (TEM) shows that the solid solution of the oxygen ranges from HfC0.98 +/- 0.01O0.02 +/- 0.03 to HfC0.90 +/- 0.01O0.10 +/- 0.03 at 1650 degrees C and from HfC0.97 +/- 0.01O0.03 +/- 0.03 to HfC0.89 +/- 0.01O0.11 +/- 0.03 at 1750 degrees C. It was then concluded that contrary with earlier previous results from the literature, the stability field of the solid solution is very limited and not very sensitive to temperature. This behavior is also in contrast with results obtained on the ZrCxOy oxycarbide which shows an isostructural form of HfCxOy. The second part of the paper reports on the first modeling of the ternary thermodynamic diagram of the C-Hf-O system by the CALPHAD method. The accurate data experimentally obtained on the solid solution were integrated as diagrammatic data for the calculation. The modeling was based on from already published binary assessments after a selection of compatible binary models and the description of the HfCxOy solid solution was then added and optimized using the data of this work. As a result, a set of coherent parameters has been obtained, allowing to calculate isothermal sections of this C-Hf-O ternary system.