In this work, a novel catalytic system is developed, consisting of palladium nanoclusters homogenously dispersed on the surface of nanostructured polymer nanofibers based on poly(L-lactic acid) (PLLA) and polyhedral oligomeric silsesquioxanes (POSS). Indeed, PLLA nanofibers containing amino-functionalized silsesquioxane molecules (POSS-NH2), potentially capable of interacting with the metal precursor, are prepared by means of electrospinning. Conversely to the polymer matrix, which does not show any tendency to retain the metal precursor, the submicrometric dispersion of POSS-NH2 in the PLLA nanofibers, as demonstrated by SEM-EDS analysis, turns out to promote the formation of metal nanoclusters. TEM measurements show a uniform distribution of Pd nanoparticles, characterized by an average dimension of ca. 4 nm, along the fibers. The prepared system proves a relevant catalytic activity toward the hydrogenation of stilbene under heterogeneous conditions. Moreover, as demonstrated by XPS measurements, the support is capable of retaining the catalyst during the hydrogenation reaction, thus preventing its leaching.