As data sets continue to increase in size, there is growing interest in methods for prediction that are both flexible and interpretable. A flurry of recent work on this topic has focused on additive modeling in the regression setting, and in particular, on the use of data-adaptive non-linear functions that can be used to flexibly model each covariate's effect, conditional on the other features in the model. In this paper, we extend this recent line of work to the survival setting. We develop an additive Cox proportional hazards model, in which each additive function is obtained by trend filtering, so that the fitted functions are piecewise polynomial with adaptively-chosen knots. An efficient proximal gradient descent algorithm is used to fit the model. We demonstrate its performance in simulations and in application to a primary biliary cirrhosis (PBC) dataset.