1. A method comprising: at a service controller for a network comprising a plurality of service nodes each configured to apply a service function to traffic that passes through the respective service node, defining a service chain identifying a set of service functions and an order in which they are applied; receiving, from a classifier, an indication that the service chain has been instantiated at the classifier; creating a service header that identifies a unique service path for the service chain, wherein the unique service path identifies both the service chain and the classifier at which the service chain is instantiated, wherein the classifier is a head-end network node for the service chain; defining, at the service controller, a plurality of identical service chains; receiving an indication that the identical service chains have been instantiated at a plurality of different classifiers; and creating unique service headers for each of the identical service chains, wherein the unique service headers each identify unique service paths for a respective one of the identical service chains instantiated at each of the plurality of classifiers, wherein each of the unique service paths identifies both the service chain and the classifier at which the service chain is instantiated.