A coarse-grain parallel multi-block algorithm was designed for CHEQNS - a multi-block solver for solving chemically reacting flows in local chemical equilibrium and has been implemented using the Message Passing Interface (MPI). The parallel implementation confirms to the Single Program Multiple Data (SPMD) model. The parallel implementation uses synchronous update of fluxes across the block-block boundaries. The solution algorithm consists of block-decoupled Gauss-Seidel iterations. The coupling between the sub-domains on different processors occurs at the Newton iteration level. The parallel implementation is general and can accept an arbitrary arrangement of blocks in multi-block configuration with multiple blocks per processor. The parallel implementation has been verified against the results from the sequential multi-block solver for different types of flows. The parallel performance has been studied in terms of speed-up and efficiency. The influence of parallelization on the convergence was also studied.