The valorization of glycerol (1), a waste of biodiesel production of Fatty Acid Methyl Esters (FAMEs), adopting a “green” approach, represents an important goal of sustainable chemistry. While the polymerization of 1 to hyperbranched oligomers is a well-established process, the linear analogues are difficult to obtain. In this context, we explore the reaction without the solvent of heterogeneous hybrid La(III)O-KIT-6 catalyst (2), which is based on lanthanum oxide on mesoporous silica gel, showing a superior linear selectivity compared to most of the analogous catalysts recently reported.