Hallucinations are a type of output error produced by deep neural networks. While this has been studied in natural language processing, they have not been researched previously in automatic speech recognition. Here, we define hallucinations in ASR as transcriptions generated by a model that are semantically unrelated to the source utterance, yet still fluent and coherent. The similarity of hallucinations to probable natural language outputs of the model creates a danger of deception and impacts the credibility of the system. We show that commonly used metrics, such as word error rates, cannot differentiate between hallucinatory and non-hallucinatory models. To address this, we propose a perturbation-based method for assessing the susceptibility of an automatic speech recognition (ASR) model to hallucination at test time, which does not require access to the training dataset. We demonstrate that this method helps to distinguish between hallucinatory and non-hallucinatory models that have similar baseline word error rates. We further explore the relationship between the types of ASR errors and the types of dataset noise to determine what types of noise are most likely to create hallucinatory outputs. We devise a framework for identifying hallucinations by analysing their semantic connection with the ground truth and their fluency. Finally, we discover how to induce hallucinations with a random noise injection to the utterance.