In existing literature, GNN training has been performed mostly in centralized, and sometimes federated, settings. In this work, we consider a fully-decentralized data-private scenario, where each node has limited knowledge of the surrounding graph. We propose the first architecture that enables GNN training in this fully-decentralized setting, by carefully combining several techniques, including decoupled learning, self-supervision and Gossip Learning. We implement two simulation tools to experimentally evaluate our solution. The results show that the proposed technique can be effectively used in scenarios where centralized or federated approaches are unfeasible or undesirable.