Getting a better understanding of user behavior is important for advancing information retrieval systems. Existing work focuses on modeling and predicting single interaction events, such as clicks. In this paper, we for the first time focus on modeling and predicting sequences of interaction events. And in particular, sequences of clicks. We formulate the problem of click sequence prediction and propose a click sequence model (CSM) that aims to predict the order in which a user will interact with search engine results. CSM is based on a neural network that follows the encoder-decoder architecture. The encoder computes contextual embeddings of the results. The decoder predicts the sequence of positions of the clicked results. It uses an attention mechanism to extract necessary information about the results at each timestep. We optimize the parameters of CSM by maximizing the likelihood of observed click sequences. We test the effectiveness of CSM on three new tasks: (i) predicting click sequences, (ii) predicting the number of clicks, and (iii) predicting whether or not a user will interact with the results in the order these results are presented on a search engine result page (SERP). Also, we show that CSM achieves state-of-the-art results on a standard click prediction task, where the goal is to predict an unordered set of results a user will click on.