By applying efficient computational algorithms to the simplest off-lattice polymer model-the freely-jointed tangent hard-sphere chain-we have been able to perform molecular dynamics simulations long enough to probe chain dynamics in the entangled regime. Chain lengths range from 8 to 192 segments while volume fractions range from 0.3 to 0.45. Analysis of the mean-square displacement (MSD), Rouse modes, scattering functions, and end-to-end vector correlations provides information about chain motion. Chain dynamics are compared with predictions of the Rouse model for short chains and the tube model of Doi and Edwards for long chains. The mean-square displacement for the inner segments of the longest chains are consistent with predictions of the tube model, reproducing : the three scaling regimes that are postulated to occur. In addition, anomalous diffusive behavior in the atomic MSD of the inner segments is observed at long times as the inner segments cross over into the free diffusion limit. Rouse-mode autocorrelation functions decay non-exponentially and do not exhibit scaling consistent with the tube model. Definitive plateau-like behaviors are observed in the density-density, correlations, normal coordinate decay, and end-to-end vector relaxation of the 192-mer fluids at the highest density.