Today's unrelenting increase in demand for information processing creates the need for novel computing concepts. Reservoir computing is such a concept that lends itself particularly well to photonic hardware implementations. Over recent years, these hardware implementations have gained maturity and now achieve state-of-the-art performance on several benchmark tasks. However, implementations so far are essentially all based on sequential data processing, leaving the inherent parallelism of photonics unexploited. Parallel implementations process all neurons simultaneously, and therefore have the potential of reducing computation time by a factor equal to the number of neurons, compared to sequential architectures. Here, we report a parallel reservoir computer that uses frequency domain multiplexing of neuron states. We illustrate its performance on standard benchmark tasks such as nonlinear channel equalization, the reproduction of a nonlinear 10th-order system, and speech recognition, obtaining error rates similar to previous optical experiments. The present experiment is thus an important step towards high speed, low footprint, all optical photonic information processing.