Machine learning as a service has given raise to privacy concerns surrounding clients' data and providers' models and has catalyzed research in private inference (PI): methods to process inferences without disclosing inputs. Recently, researchers have adapted cryptographic techniques to show PI is possible, however all solutions increase inference latency beyond practical limits. This paper makes the observation that existing models are ill-suited for PI and proposes a novel NAS method, named CryptoNAS, for finding and tailoring models to the needs of PI. The key insight is that in PI operator latency cost are non-linear operations (e.g., ReLU) dominate latency, while linear layers become effectively free. We develop the idea of a ReLU budget as a proxy for inference latency and use CryptoNAS to build models that maximize accuracy within a given budget. CryptoNAS improves accuracy by 3.4% and latency by 2.4x over the state-of-the-art.