Aspect-Sentiment Triplet Extraction (ASTE) is one of the most challenging and complex tasks in sentiment analysis. It concerns the construction of triplets that contain an aspect, its associated sentiment polarity, and an opinion phrase that serves as a rationale for the assigned polarity. Despite the growing popularity of the task and the many machine learning methods being proposed to address it, the number of datasets for ASTE is very limited. In particular, no dataset is available for any of the Slavic languages. In this paper, we present two new datasets for ASTE containing customer opinions about hotels and purchased products expressed in Polish. We also perform experiments with two ASTE techniques combined with two large language models for Polish to investigate their performance and the difficulty of the assembled datasets. The new datasets are available under a permissive licence and have the same file format as the English datasets, facilitating their use in future research.