Molecular dynamics (MD) is used to simulate a model atactic poly(methyl methacrylate) (PMMA) system in which carbon nanotubes (CNTs) have been randomly dispersed. Our purpose is to elucidate the equilibrium structure and dynamic behavior of PMMA chains at the interface with a CNT. CNTs with different diameters and at different concentrations in the host PMMA matrix are studied, and their effect on the equilibrium squared radius-of-gyration and squared end-to-end distance of PMMA chains is examined. We have analyzed PMMA density, structure, and conformation both axially and normal to the CNT surface. Our MD simulations indicate that the presence of CNTs causes a small decrease in the size of the polymer chains, which becomes more pronounced as the concentration (volume fraction) and diameter of CNTs in the nanocomposite increases. We also provide a detailed analysis of adsorbed PMMA chain conformations in terms of trains, loops, and tails, and their statistical properties. An important finding of our work is that PMMA chains tend to penetrate significantly into the CNTs through their faces; as a result of CNT filling by PMMA chains, the area near the CNT mouths is characterized by significantly higher polymer mass density (almost by 45%) than the bulk of the nanocomposite. Additional simulation results for local and terminal relaxation in the PMMA-CNT nanocomposites reveal that due to strong PMMA-CNT attractive forces, all relaxation times in the interfacial region are significantly prolonged in comparison to the bulk, and the same happens with the diffusive (translational) motion of the chains. The density profile that develops (both axially and radially) in the vicinity of CNTs appears to significantly delay PMMA dynamics at all length scales. How this affects the glass-transition temperature of the nanocomposite is also analyzed.