A comparative study of time integration methods for the Navier-Stokes equations with chemistry is presented. A hybrid line-relaxation and point-relaxation implicit method is compared with a fully-coupled time integration method. The fully-coupled method makes use of the PETSc library and uses a Krylov method with an additive Schwarz method for parallel solutions. Computations are presented for a blunt-body flow over a range of Reynolds numbers, and results show that the hybrid line/point-relaxation and the fullycoupled methods both converge to steady state independent of the free-stream Reynolds number and grid stretching. The approximate hybrid method converges in less CPU time in this case. Memory usage and elapsed CPU time results are shown for perfect-gas and 11 species air chemistry calculations. The memory requirements triple when the fully-coupled method is used for both equation sets. Results also show that the fully-coupled method is superior to the approximate method when the flow is strongly anisotropic or when the mesh topology is not designed to take advantage of the hybrid method.