Hyperledger Fabric is a permissioned blockchain architecture, providing a consistent distributed ledger, shared by a set of peers that must all have the same view of its state. For many applications, it is desirable to keep private data on the ledger, but the same-view principle makes it challenging to implement. In this paper, we explore supporting private data on Fabric using secure multiparty computation (MPC). In our solution, peers encrypt their private data before storing it on the chain and use secure MPC whenever such private data are needed in a transaction. We created a demo of our solution, implementing a bidding system where sellers list assets on the ledger with a secret reserve price, and bidders publish their bids on the ledger but keep secret the bidding price. We implemented a smart contract that runs the auction on this secret data, using a simple secure-MPC protocol that was built using the EMP-toolkit library. We identified two basic services that should be added to Hyperledger Fabric to support our solution, inspiring follow-up work to implement and add these services to the Hyperledger Fabric architecture.