Future networks are expected to support cross-domain, cost-aware and fine-grained services in an efficient and flexible manner. Service Function Chaining (SFC) has been introduced as a promising approach to deliver these services. In the literature, centralized resource orchestration is usually employed to process SFC requests and manage computing and network resources. However, centralized approaches inhibit the scalability and domain autonomy in multi-domain networks. They also neglect location and hardware dependencies of service chains. In this paper, we propose Distributed Federated Service Chaining (DFSC), a framework for orchestrating and maintaining SFC placement in a distributed fashion while sharing only a minimal amount of domain information and control. First, a deployment cost minimization problem is formulated as an Integer Linear Programming (ILP) problem with fine-grained constraints for location and hardware dependencies. We show that this problem is NP-hard. Then, a placement algorithm is devised to use information only on inter-domain paths and border nodes. Our extensive experimental results demonstrate that DFSC efficiently optimizes the deployment cost, supports domain autonomy and enables faster decision-making. The results also show that DFSC finds solutions within a factor 1.15 of the optimal solution on average. Compared to a centralized approach in the literature, DFSC reduces the deployment cost by up to 20% and uses 70% less decision-making time.