With the rapid increase of mobile devices and online media, more and more people prefer posting/viewing videos online. Generally, these videos are presented on video streaming sites with image thumbnails and text titles. While facing huge amounts of videos, a viewer clicks through a certain video with high probability because of its eye-catching thumbnail. However, current video thumbnails are created manually, which is time-consuming and quality-unguaranteed. And static image thumbnails contain very limited information of the corresponding videos, which prevents users from successfully clicking what they really want to view. In this paper, we address a novel problem, namely GIF thumbnail generation, which aims to automatically generate GIF thumbnails for videos and consequently boost their Click-Through-Rate (CTR). Here, a GIF thumbnail is an animated GIF file consisting of multiple segments from the video, containing more information of the target video than a static image thumbnail. To support this study, we build the first GIF thumbnails benchmark dataset that consists of 1070 videos covering a total duration of 69.1 hours, and 5394 corresponding manually-annotated GIFs. To solve this problem, we propose a learning-based automatic GIF thumbnail generation model, which is called Generative Variational Dual-Encoder (GEVADEN). As not relying on any user interaction information (e.g. time-sync comments and real-time view counts), this model is applicable to newly-uploaded/rarely-viewed videos. Experiments on our built dataset show that GEVADEN significantly outperforms several baselines, including video-summarization and highlight-detection based ones. Furthermore, we develop a pilot application of the proposed model on an online video platform with 9814 videos covering 1231 hours, which shows that our model achieves a 37.5% CTR improvement over traditional image thumbnails. This further validates the effectiveness of the proposed model and the promising application prospect of GIF thumbnails.