Differential privacy offers a formal privacy guarantee for individuals, but many deployments of differentially private systems require a trusted third party (the data curator). We propose DuetSGX, a system that uses secure hardware (Intel's SGX) to eliminate the need for a trusted data curator. Data owners submit encrypted data that can be decrypted only within a secure enclave running the DuetSGX system, ensuring that sensitive data is never available to the data curator. Analysts submit queries written in the Duet language, which is specifically designed for verifying that programs satisfy differential privacy; DuetSGX uses the Duet typechecker to verify that each query satisfies differential privacy before running it. DuetSGX therefore provides the benefits of local differential privacy and central differential privacy simultaneously: noise is only added to final results, and there is no trusted third party. We have implemented a proof-of-concept implementation of DuetSGX and we release it as open-source.