Complex inter-connections of virtual functions form the so-called Service Function Chains (SFCs) deployed in the Cloud. Such service chains are used for critical services like e-health or autonomous transportation systems and thus require high availability. Respecting some availability level is hard in general, but it becomes even harder if the operator of the service is not aware of the physical infrastructure that will support the service, which is the case when SFCs are deployed in multi-tenant data centers. In this paper, we propose an algorithm to solve the placement of topology-oblivious SFC demands such that placed SFCs respect availability constraints imposed by the tenant. The algorithm leverages Fat-Tree properties to be computationally doable in an online manner. The simulation results show that it is able to satisfy as many demands as possible by spreading the load between the replicas and enhancing the network resources utilization.