We introduce HunSum-1: a dataset for Hungarian abstractive summarization, consisting of 1.14M news articles. The dataset is built by collecting, cleaning and deduplicating data from 9 major Hungarian news sites through CommonCrawl. Using this dataset, we build abstractive summarizer models based on huBERT and mT5. We demonstrate the value of the created dataset by performing a quantitative and qualitative analysis on the models' results. The HunSum-1 dataset, all models used in our experiments and our code are available open source.