We explore the dynamics of entangled polymer chains embedded into nanocomposites. From primitive path analysis, highly entangled polymer chains are found to be significantly disentangled during increment of the volume fraction of spherical nonattractive nanoparticles (NPs) from 0 to 42%. A critical volume fraction, ϕ(c)=31%, is found to control the crossover from polymer chain entanglements to "NP entanglements." While below ϕ(c), the polymer chain relaxation accelerates upon filling, above ϕ(c), the situation reverses: polymer dynamics becomes geometrically constrained upon adding NPs. Our findings provide a microscopic understanding of the dynamics of entangled polymer chains inside their composites, and offer an explanation for the unusual rheological properties of polymer composites.