End-to-end encrypted messaging applications such as Signal became widely popular thanks to their capability to ensure the confidentiality and integrity of online communication. While the highest security guarantees were long reserved to two-party communication, solutions for n-party communication remained either inefficient or less secure until the standardization of the MLS Protocol (Messaging Layer Security). This new protocol offers an efficient way to provide end-to-end secure communication with the same guarantees originally offered by the Signal Protocol for two-party communication. However, both solutions still rely on a centralized component for message delivery, called the Delivery Service in the MLS Protocol. The centralization of the Delivery Service makes it an ideal target for attackers and threatens the availability of any protocol relying on MLS. In order to overcome this issue, we propose the design of a fully distributed Delivery Service that allows clients to exchange protocol messages efficiently and without any intermediary. It uses a Probabilistic Reliable-Broadcast mechanism to efficiently deliver messages and the Cascade Consensus Protocol to handle messages requiring an agreement. Our solution strengthens the availability of the MLS Protocol without compromising its security.