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Researchers have long struggled to identify causal effects in nonexperimental settings. Many recently proposed strategies assume ignorability of the treatment assignment mechanism and require fitting two models—one for the assignment mechanism and one for the response surface. This article proposes a strategy that instead focuses on very flexibly modeling just the response surface using a Bayesian nonparametric modeling procedure, Bayesian Additive Regression Trees (BART). BART has several advantages: it is far simpler to use than many recent competitors, requires less guesswork in model fitting, handles a large number of predictors, yields coherent uncertainty intervals, and fluidly handles continuous treatment variables and missing data for the outcome variable. BART also naturally identifies heterogeneous treatment effects. BART produces more accurate estimates of average treatment effects compared to propensity score matching, propensity-weighted estimators, and regression adjustment in the nonlinear simulation situations examined. Further, it is highly competitive in linear settings with the “correct” model, linear regression. Supplemental materials including code and data to replicate simulations and examples from the article as well as methods for population inference are available online.