Combining elastic incoherent neutron scattering experiments at different resolutions with molecular dynamics simulations, we report the observation of a protein-like dynamical transition in linear chains of Poly(N-isopropylacrylamide). We identify the onset of the transition at a temperature $T_d$ of about 225~K. Thanks to a novel global fit procedure, we find quantitative agreement between measured and calculated polymer mean-squared displacements at all temperatures and time resolutions. Our results confirm the generality of the dynamical transition in macromolecular systems in aqueous environments, independently of the internal polymer topology.