The chain represents the house and line of David - the genealogy of Jesus.
"So Joseph also went up from the town of Nazareth in Galilee to Judea, to Bethlehem the town of David, because he belonged to the house and line of David."
It was promised that the Messiah would come from the house of David and be born in Bethlehem.
In Matthew chapter one the genealogy of Jesus is recorded from Abraham all the way to Joseph. In Luke chapter three the genealogy of begins with Jesus and goes all the way back to God Himself. The two differ slightly, one tracing the line from David to Mary, the other tracing the line from David to Joseph.