The chain dynamics of co(acrylic‐styrene)/montmorillonite (MMT) nanoclay nanocomposites in the melt was studied by shear rheometry. Copolymers containing 60% butyl acrylate (BA), 38% styrene (sty), and 2% methacrylic acid (MAA) were synthesized in the presence of MMT nanoclay, that is, in‐situ, and the MMT content ranged from cMMT = 5–25 wt%. Recently, it was shown that nanoclay was exfoliated when cMMT ≤ 5 wt% and intercalated at higher concentrations, and the tensile modulus increased over an order of magnitude with MMT content [Romo‐Uribe, Polym Adv Technol, 2021]. Here, the chain dynamics was investigated using shearrheology. The results revealed that nanoclay slowed down the chain dynamics in the terminal regime, the terminal relaxation time τt increased up to an order of magnitude. Furthermore, nanoclay induced 10‐fold increase of rubbery modulus Ge with the consequent reduction of molecular weight between entanglements Me and reduction of packing length p. Furthermore, the nanoconfinement imposed on the polymer chains reduced the energy dissipation in the transition regime (as indicated by the damping tan δ) thus correlating with the increase of the glass transition temperature, Tg. Therefore, understanding and controlling nanoconfinement and its influence on chain dynamics would enable tuning the physical properties of polymer‐clay nanocomposites.