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Predictive business process monitoring increasingly leverages sophisticated prediction models. Although sophisticated models achieve consistently higher prediction accuracy than simple models, one major drawback is their lack of interpretability, which limits their adoption in practice. We thus see growing interest in explainable predictive business process monitoring, which aims to increase the interpretability of prediction models. Existing solutions focus on giving factual explanations.While factual explanations can be helpful, humans typically do not ask why a particular prediction was made, but rather why it was made instead of another prediction, i.e., humans are interested in counterfactual explanations. While research in explainable AI produced several promising techniques to generate counterfactual explanations, directly applying them to predictive process monitoring may deliver unrealistic explanations, because they ignore the underlying process constraints. We propose LORELEY, a counterfactual explanation technique for predictive process monitoring, which extends LORE, a recent explainable AI technique. We impose control flow constraints to the explanation generation process to ensure realistic counterfactual explanations. Moreover, we extend LORE to enable explaining multi-class classification models. Experimental results using a real, public dataset indicate that LORELEY can approximate the prediction models with an average fidelity of 97.69\% and generate realistic counterfactual explanations.