Virtual synchrony is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is a key criterion for the success of such implementations. This is because large distributed systems can be highly available as long as they do not depend on the full operational status of every system participant. Namely, they employ redundancy in numbers to overcome non-optimal behavior of participants and to gain global robustness and high availability. Self-stabilizing systems can tolerate transient faults that drive the system to an arbitrary unpredicted configuration. Such systems automatically regain consistency from any such arbitrary configuration, and then produce the desired system behavior. Practically self-stabilizing systems ensure the desired system behavior for practically infinite number of successive steps e.g., $2^{64}$ steps. We present the first practically self-stabilizing virtual synchrony algorithm. The algorithm is a combination of several new techniques that may be of independent interest. In particular, we present a new counter algorithm that establishes an efficient practically unbounded counter, that in turn can be directly used to implement a self-stabilizing Multiple-Writer Multiple-Reader (MWMR) register emulation. Other components include self-stabilizing group membership, self-stabilizing multicast, and self-stabilizing emulation of replicated state machine. As we base the replicated state machine implementation on virtual synchrony, rather than consensus, the system progresses in more extreme asynchronous executions in relation to consensus-based replicated state machine.