Okay, here's the deal.
The Lodge Chief can, but does not necessarily, serve as a member of the Council Camping Committee. For example, my Council asks the lodge chief to serve as one of two allowed youth representatives to the Council Executive Board. There is no definitive method for where the Lodge Chief can serve--while the National OA Committee suggests that he serve as a member of the Camping Committee, this is a case of "If the local system works fine, Irving isn't likely to interfere."
If, and only if, the Lodge Chief is asked to serve anywhere at the Council level, such as on the two positions I mentioned, he should wear silver shoulder loops, no unit numerals, and the council-level POR patch for the position he's serving in (after filling out an adult registration form). He should continue to maintain a uniform for unit wear, and wear that uniform when he is functioning outside of his Lodge Chief responsibilities (so, second uniform shirt suggested). This unit uniform should reflect his current status within the unit, including unit numerals, a unit POR patch, and olive/blaze loops (for troop/team, respectively).
(Interesting fact: there are no OA National Chief or National Vice Chief POR patches, nor do they particularly like the Lodge Chief patches. See here for an explanation: http://www.oa-bsa.org/features/chairman/answer5.htm)
If the Lodge Chief is not asked to serve at the Council level (rare, but it does happen), he should continue to wear the unit insignia with olive/blaze loops, even while functioning as Lodge Chief, as an Arrowman's first responsibility is to his unit.
As previously mentioned, only regional officers and local council professional staffers wear the region insignia, so the lodge chief is not permitted to wear this piece of cloth. Generally, the only OA youth allowed to wear this is the Region Chief, as all Regions allow the Region Chief to serve on the Region Committee.
The above standards hold true for Chapter Chief, provided you replace Council with District at the appropriate spaces.(This message has been edited by jdbsa05)