A smart contract on a blockchain cannot keep a secret because its data is replicated on all nodes in a network. To remedy this problem, it has been suggested to combine blockchains with trusted execution environments (TEEs), such as Intel SGX, for executing applications that demand privacy. Untrusted blockchain nodes cannot get access to the data and computations inside the TEE. This paper first explores some pitfalls that arise from the combination of TEEs with blockchains. Since TEEs are, in principle, stateless they are susceptible to rollback attacks, which should be prevented to maintain privacy for the application. However, in blockchains with non-final consensus protocols, such as the proof-of-work in Ethereum and others, the contract execution must handle rollbacks by design. This implies that TEEs for securing blockchain execution cannot be directly used for such blockchains; this approach works only when the consensus decisions are final. Second, this work introduces an architecture and a prototype for smart-contract execution within Intel SGX technology for Hyperledger Fabric, a prominent platform for enterprise blockchain applications. Our system resolves difficulties posed by the execute-order-validate architecture of Fabric and prevents rollback attacks on TEE-based execution as far as possible. For increasing security, our design encapsulates each application on the blockchain within its own enclave that shields it from the host system. An evaluation shows that the overhead moving execution into SGX is within 10%-20% for a sealed-bid auction application.