Deploying Internet of Things (IoT)-enabled virtual network function (VNF) chains to Cloud-Edge infrastructures requires determining a placement for each VNF that satisfies all set deployment requirements as well as a software-defined routing of traffic flows between consecutive functions that meets all set communication requirements. In this article, we present a declarative solution, EdgeUsher, to the problem of how to best place VNF chains to Cloud-Edge infrastructures. EdgeUsher can determine all eligible placements for a set of VNF chains to a Cloud-Edge infrastructure so to satisfy all of their hardware, IoT, security, bandwidth, and latency requirements. It exploits probability distributions to model the dynamic variations in the available Cloud-Edge infrastructure and to assess output eligible placements against those variations.