The N2 + N2 → N2 +N +N dissociation reaction plays an important role in hypersonic flows in the atmosphere. We are studying this reaction using the quasiclassical trajectory method (QCT). We computed trajectories over a range of translational and rovibrational temperatures. The simulations use a new, recently published potential energy surface for the N4 system. The surface was constructed from ab initio electronic structure calculations using complete-active-space second-order perturbation theory (CASPT2) and was fit by analytic functions using permutationally-invariant polynomials. For the QCT calculations, the initial rotational and vibrational states of the N2 reactants are obtained by sampling from a two-temperature ensemble of all quantized bound and quasibound states. All initial parameters are sampled randomly from appropriate distributions, and trajectories are propagated to compute thermal and ensemble-averaged cross sections and reaction rates. After reviewing the methodology, we discuss preliminary results from our calculations, including considerations of statistical convergence and uncertainty. Our reaction rates show reasonable agreement with past research, and they show strong dependence of the reaction rate on the rovibrational temperature. We plan to use ongoing QCT analyses to better inform macroscopic models for computational fluid dynamics simulations of hypersonic reacting flows.