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• Formalizing the novel problem of data poisoning of counterfactual explanations. • Investigating the effect of data poisoning on counterfactuals. • Many state-of-the-art methods are vulnerable to data poisoning. Counterfactual explanations are a widely used approach for examining the predictions of black-box systems. They can offer the opportunity for computational recourse by suggesting actionable changes on how to alter the input to obtain a different (i.e., more favorable) system output. However, recent studies have pointed out their susceptibility to various forms of manipulation. This work studies the vulnerability of counterfactual explanations to data poisoning. We formally introduce and investigate data poisoning in the context of counterfactual explanations for increasing the cost of recourse on three different levels: locally for a single instance, a sub-group of instances, or globally for all instances. In this context, we formally introduce and characterize data poisonings, from which we derive and investigate a general data poisoning mechanism. We demonstrate the impact of such data poisoning in the critical real-world application of explaining event detections in water distribution networks. Additionally, we conduct an extensive empirical evaluation, demonstrating that state-of-the-art counterfactual generation methods and toolboxes are vulnerable to such data poisoning. Furthermore, we find that existing defense methods fail to detect those poisonous samples.