Service Function Chaining (SFC) enables dynamic and adaptive network service provisioning. However, virtual infrastructure providers are reluctant to disclose SFC APIs and infrastructure monitoring information to tenants, therefore undermining tenants’ capability in dynamically and flexibly managing application-tailored network services. In this work, we provide a two-fold contribution to the problem of tenant-defined service function chaining on a multi-site virtual infrastructure, which has not been widely investigated yet. First, we propose a VNF Selection algorithm that relies on an abstracted network model thus minimizing topological and monitoring information required by the infrastructure. Our algorithm selects a set of VNF instances that minimizes the end-to-end latency (accounting for network and processing delay) and also guarantees that already established chains do not violate their maximum latency constraint due to the additional load at VNFs brought by new chain requests. Second, we describe an SFC solution composed of an SFC application that uses our VNF Selection algorithm and a forwarding mechanism that manages chains and controls traffic steering within the tenant network without leveraging infrastructure control APIs. Validation and comparative evaluations are performed through simulations. Finally, the proposed approach is assessed through a set of experiments carried out on a multi-site testbed infrastructure.