This paper proposes Concurrent-Access Obfuscated Store (CAOS), a construction for remote data storage that provides access-pattern obfuscation in a honest-but-curious adversarial model, while allowing for low bandwidth overhead and client storage. Compared to the state of the art, the main advantage of CAOS is that it supports concurrent access without a proxy, for multiple read-only clients and a single read-write client. Concurrent access is achieved by letting clients maintain independent maps that describe how the data is stored. These maps might diverge from client to client, but it is guaranteed that no client will ever lose track of current data. We achieve efficiency and concurrency at the expense of perfect obfuscation: in CAOS the extent to which access patterns are hidden is determined by the resources allocated to its built-in obfuscation mechanism. To assess this trade-off we provide both a security and a performance analysis of our protocol instance. We additionally provide a proof-of-concept implementation.