We present an extension of our graphics processing units (GPU)-accelerated quantum chemistry package to employ OpenCL compute kernels, which can be executed on a wide range of computing devices like CPUs, Intel Xeon Phi, and AMD GPUs. Here, we focus on the use of AMD GPUs and discuss differences as compared to CUDA-based calculations on NVIDIA GPUs. First illustrative timings are presented for hybrid density functional theory calculations using serial as well as parallel compute environments. The results show that AMD GPUs are as fast or faster than comparable NVIDIA GPUs and provide a viable alternative for quantum chemical applications.