Process mining generates valuable insights into business processes through the analysis of event logs. However, event logs are commonly subject to various data quality issues which hinder the success of process mining initiatives in organizations. Identical timestamp errors, for example, occur when multiple events of a process instance mistakenly share the same timestamp. This error causes discovered process models to be unrepresentative and process performance analysis results to be misleading. To address this problem, we propose a method for automatically repairing identical timestamp errors in event logs. To that end, we combine existing method components for error detection and reordering of erroneous events with a novel approach for repairing timestamps based on Generative Adversarial Networks. To allow for a rigorous evaluation, we instantiate our approach as a software prototype, and use it to repair a total of six real-life and artificial event logs with overall 30 variations. Thereby, we show that the proposed method shows improved results compared to alternative approaches for repairing identical timestamp errors in event logs.