This paper introduces GreekCommonGen, the first benchmark designed for generative commonsense reasoning in Greek. The dataset is created by automatically translating the original English CommonGen corpus and subsequently refining the outputs through manual post-editing to ensure linguistic and semantic quality. We conduct a comprehensive evaluation of a range of approaches/models on this benchmark, exploring the impact of different prompting strategies, decoding methods, and model sizes/architectures. Our findings provide valuable insights into the challenges of commonsense generation in Greek, paving the way for future research in the field.