Provided are a computer program product, system, and method for deduplicating chunk digests received for chunks in objects in objects provided by clients to store in a storage. An index has chunk signatures calculated from chunks of data in the data objects in the storage. A transaction requests a shared lock for a chunk digest calculated from a chunk in an object to add to the storage. In response to not receiving the shared lock, the transaction is granted a shared lock to the chunk digest in wait mode. The transaction does not proceed until being granted the shared lock. In response to receiving the shared lock, a determination is made as to whether the chunk digest is in the index. A reference to the chunk data is provided for the object when the chunk digest is indicated in the index.