The Community Multiscale Air Quality (CMAQ) model simulates atmospheric phenomena, including advection, diffusion, gas-phase chemistry, aerosol physics and chemistry, and cloud processes. Gas-phase chemistry is often a major computational bottleneck due to its representation as large systems of coupled nonlinear stiff differential equations. We leverage the parallel computational performance of graphics processing unit (GPU) hardware to accelerate the numerical integration of these systems in CMAQ's CHEM module. Our implementation, dubbed CMAQ-CUDA, in reference to its use in the Compute Unified Device Architecture (CUDA) general purpose GPU (GPGPU) computing solution, migrates CMAQ's Rosenbrock solver from Fortran to CUDA Fortran. CMAQ-CUDA accelerates the Rosenbrock solver such that simulations using the chemical mechanisms RACM2, CB6R5, and SAPRC07 require only 51%, 50%, or 35% as much time, respectively, as CMAQv5.4 to complete a chemistry time step. Our results demonstrate that CMAQ is amenable to GPU acceleration and highlight a novel Rosenbrock solver implementation for reducing the computational burden imposed by the CHEM module.