Responsive (smart, intelligent, adaptive) polymers have been widely explored for a variety of advanced applications in recent years. The thermoresponsive poly(N,N-diethylacrylamide) (PDEAAm), which has a better biocompatibility than the widely investigated poly(N,N-isopropylacrylamide), has gained increased interest in recent years. In this paper, the successful synthesis, characterization, and bioconjugation of a novel thermoresponsive copolymer, poly(N,N-diethylacrylamide-co-glycidyl methacrylate) (P(DEAAm-co-GMA)), obtained by free radical copolymerization with various comonomer contents and monomer/initiator ratios are reported. It was found that all the investigated copolymers possess LCST-type thermoresponsive behavior with small extent of hysteresis, and the critical solution temperatures (CST), i.e., the cloud and clearing points, decrease linearly with increasing GMA content of these copolymers. The P(DEAAm-co-GMA) copolymer with pendant epoxy groups was found to conjugate efficiently with α-chymotrypsin in a direct, one-step reaction, leading to enzyme–polymer nanoparticle (EPNP) with average size of 56.9 nm. This EPNP also shows reversible thermoresponsive behavior with somewhat higher critical solution temperature than that of the unreacted P(DEAAm-co-GMA). Although the catalytic activity of the enzyme–polymer nanoconjugate is lower than that of the native enzyme, the results of the enzyme activity investigations prove that the pH and thermal stability of the enzyme is significantly enhanced by conjugation the with P(DEAAm-co-GMA) copolymer.