The estimation of treatment effects is a pervasive problem in medicine. Existing methods for estimating treatment effects from longitudinal observational data assume that there are no hidden confounders. This assumption is not testable in practice and, if it does not hold, leads to biased estimates. In this paper, we develop the Time Series Deconfounder, a method that leverages the assignment of multiple treatments over time to enable the estimation of treatment effects in the presence of multi-cause hidden confounders. The Time Series Deconfounder uses a novel recurrent neural network architecture with multitask output to build a factor model over time and infer substitute confounders that render the assigned treatments conditionally independent. Then it performs causal inference using the substitute confounders. We provide a theoretical analysis for obtaining unbiased causal effects of time-varying exposures using the Time Series Deconfounder. Using both simulations and real data to show the effectiveness of our method in deconfounding the estimation of treatment responses in longitudinal data.