A model poly(ethylene oxide) (PEO)/laponite hybrid material, characterized by a high silicate content, was used to probe the dynamical behavior of polymer chains at the surface with clay platelets. Such a system mimics the intercalated phases that may occur in polymer/clay nanocomposites with usual silicate amounts of 5 wt %. The segmental motions underlying the α-relaxation of fully amorphous PEO chains confined within the nanometer-thick laponite galleries were monitored over the tens of microseconds time scale by means of 13C and 1H solid-state NMR. A significant slowing down of these motions was mostly observed, as compared to the local dynamics in the amorphous phase of neat PEO. Strong dynamical heterogeneities among the intercalated PEO monomer units remain even at room temperature, i.e., more than 50 K above the temperature at which the frequency of the segmental motions displayed by a significant part of the PEO chain segments gets above 52 kHz. Such heterogeneities are related to a pronounced extension of the α-relaxation process toward the low-frequency side. The slowing down of the PEO segmental motions was assigned to ion-dipole interactions between the PEO oxygen atoms and the Na+ counterions located in the laponite galleries. The domains formed by PEO monomer units characterized by a reduced segmental mobility were found to display rather long lifetime, about 13 ms at room temperature.