After his studies at the École normale supérieure in Paris, Chabbal began his career as a physician.

There, he founded the Programme interdisciplinaire de recherche pour l'énergie solaire (PIRDES), of which he became the director.

He was Director General of the CNRS from 1976 to 1979, and gave great importance to the engineering sciences while in office.

From 2005 to 2007, he worked in the ministerial cabinet of François Goulard and helped create Label Carnot.

He worked on several boards of directors, including Saint-Gobain, ANVAR, and the French Institute for Research in Computer Science and Automation.