In this study, we investigated the influence of methacryl-functionalized polyhedral oligomeric silsesquioxane (MA-POSS) nanoparticles as a plasticizer and thermal stabilizer for a poly(vinyl chloride) (PVC) homopolymer and for a poly(vinyl chloride)/dissononyl cyclohexane-1,2-dicarboxylate (PVC/DINCH) binary blend system. The PVC and the PVC/DINCH blend both became flexible, with decreases in their glass transition temperatures and increases in their thermal decomposition temperatures, upon an increase in MA-POSS content, the result of hydrogen bonding between the C=O groups of MA-POSS and the H–CCl units of the PVC, as determined using infrared spectroscopy. Furthermore, the first thermal decomposition temperature of the pure PVC, due to the emission of HCl, increased from 290 to 306 °C, that is, the MA-POSS nanoparticles had a retarding effect on the decomposition of the PVC matrix. In tensile tests, all the PVC/DINCH/MA-POSS ternary blends were transparent and displayed flexibility, but their modulus and tensile strength both decreased, while their elongation properties increased, upon an increase in MA-POSS concentration, both before and after thermal annealing. In contrast, the elongation decreased, but the modulus and tensile strength increased, after thermal annealing at 100 °C for 7 days.