A new framework to perform routing at the autonomous system (AS) level is proposed here. This mechanism, called chain routing framework (CRF), uses complete orders as its main topological unit. Since complete orders are acyclic digraphs that possess a known topology, it is possible to use these acyclic structures to route consistently packets between a group of ASs. The adoption of complete orders also allows easy identification and avoidance of persistent route oscillations, eliminates the possibility of developing transient loops in paths and provides a structure that facilitates the implementation of traffic engineering. Moreover, by combining CRF with other mechanisms that implement complete orders in time, the authors propose that it is possible to design a new routing protocol, which can be more reliable and stable than the border gateway protocol.