Accurate prediction of suitable discourse connectives (however, furthermore, etc.) is a key component of any system aimed at building coherent and fluent discourses from shorter sentences and passages. As an example, a dialog system might assemble a long and informative answer by sampling passages extracted from different documents retrieved from the web. We formulate the task of discourse connective prediction and release a dataset of 2.9M sentence pairs separated by discourse connectives for this task. Then, we evaluate the hardness of the task for human raters, apply a recently proposed decomposable attention (DA) model to this task and observe that the automatic predictor has a higher F1 than human raters (32 vs. 30). Nevertheless, under specific conditions the raters still outperform the DA model, suggesting that there is headroom for future improvements. Finally, we further demonstrate the usefulness of the connectives dataset by showing that it improves implicit discourse relation prediction when used for model pre-training.