This document proposes a method called Constrained Server Chaining (CSC) to optimize CDN infrastructure for live streaming. CSC allows CDN streaming servers to dynamically select upstream servers to pull live streams from, rather than only pulling from fixed ingest servers. This allows streaming servers to form constrained chains to minimize total transit costs for the CDN provider while ensuring end user experience is not compromised by capping delivery path lengths. The document outlines the problem definition, design overview, and software architecture of CSC and provides an example to motivate how CSC can reduce costs compared to traditional layered CDN structures.