In this work, we define the task of teaser generation and provide an evaluation benchmark and baseline systems for the process of generating teasers. A teaser is a short reading suggestion for an article that is illustrative and includes curiosity-arousing elements to entice potential readers to read particular news items. Teasers are one of the main vehicles for transmitting news to social media users. We compile a novel dataset of teasers by systematically accumulating tweets and selecting those that conform to the teaser definition. We have compared a number of neural abstractive architectures on the task of teaser generation and the overall best performing system is See et al. seq2seq with pointer network.