Nanoparticles present a new frontier for understanding polymer dynamics in complex, nanoscale environments. We report that the addition of single-walled carbon nanotubes(SWCNTs) produces a minimum in the diffusion coefficient with increasing nanoparticle concentration, phi. Initially, tracer diffusion coefficients (D) are suppressed with increasing phi and then increase beyond a critical concentration, phi(crit) < 1 vol %. Shorter tracer chains exhibit a greater slowing down than longer chains, whereas longer matrix chains decrease the value of phi(crit). The experimental results are discussed in terms of locally anisotropic diffusion perpendicular and parallel to the nanotube Filler and Simulated using a trap model that defines a trap size and the extent of slowing perpendicular to the cylindrical trap. The simulated diffusion coefficients capture both the initial decrease in D attributed to isolated traps and the recovery of D above phi(crit) corresponding to trap percolation. Nanoparticles influence polymer diffusion in fascinating ways and will refine our understanding of polymer reptation and might also inform the study of biopolymer diffusion in living systems.