Hallucination of text ungrounded in the input is a well-known problem in neural data-to-text generation. Many methods have been proposed to mitigate it, but they typically require altering model architecture or collecting additional data, and thus cannot be easily applied to an existing model. In this paper, we explore a new way to mitigate hallucinations by combining the probabilistic output of a generator language model (LM) with the output of a special "text critic" classifier, which guides the generation by assessing the match between the input data and the text generated so far. Our method does not need any changes to the underlying LM's architecture or training procedure and can thus be combined with any model and decoding operating on word probabilities. The critic does not need any additional training data, using the base LM's training data and synthetic negative examples. Our experimental results show that our method improves over the baseline on the WebNLG and OpenDialKG benchmarks.