Patient data is widely used to estimate heterogeneous treatment effects and understand the effectiveness and safety of drugs. Yet, patient data includes highlysensitive information that must be kept private. In this work, we aim to estimatethe conditional average treatment effect (CATE) from observational data underdifferential privacy. Specifically, we present DP-CATE, a novel framework forCATE estimation that is Neyman-orthogonal and ensures differential privacy of the estimates. Our framework is highly general: it applies to any two-stageCATE meta-learner with a Neyman-orthogonal loss function and any machinelearning model can be used for nuisance estimation. We further provide an extension of our DP-CATE, where we employ RKHS regression to release the completeCATE function while ensuring differential privacy. We demonstrate the effectiveness of DP-CATE across various experiments using synthetic and real-worlddatasets. To the best of our knowledge, we are the first to provide a framework forCATE estimation that is doubly robust and differentially private.