With social media becoming increasingly popular on which lots of news and real-time events are reported, developing automated question answering systems is critical to the effectiveness of many applications that rely on real-time knowledge. While previous datasets have concentrated on question answering (QA) for formal text like news and Wikipedia, we present the first large-scale dataset for QA over social media data. To ensure that the tweets we collected are useful, we only gather tweets used by journalists to write news articles. We then ask human annotators to write questions and answers upon these tweets. Unlike other QA datasets like SQuAD in which the answers are extractive, we allow the answers to be abstractive. We show that two recently proposed neural models that perform well on formal texts are limited in their performance when applied to our dataset. In addition, even the fine-tuned BERT model is still lagging behind human performance with a large margin. Our results thus point to the need of improved QA systems targeting social media text.