This is possible via OpenStack Object Storage (code-named Swift), which is open source software for creating redundant, scalable object storage using clusters of standardized servers, specifically its recently added (optional) S3 API layer, which emulates the S3 REST API on top of Object Storage.
See Configuring Object Storage with the S3 API for the official documentation - a more insightful and illustrated small tutorial regarding the entire setup is available in S3 APIs on OpenStack Swift (which builds on the more complex Installing an OpenStack Swift cluster on EC2 though).
Update
An noteworthy alternative is Ceph, which is a unified, distributed storage system designed for excellent performance, reliability and scalability - interestingly it provides all three common storage models, i.e. Object Storage, Block Storage and a File System and the RADOS Gateway provides Amazon S3 and OpenStack Swift compatible interfaces to the RADOS object store [emphasis mine], see RADOS S3 API for details on currently supported S3 API features.