Bill, I'm assuming the authorities in SA wanted to see the RENAR form from Argentina as well as your US Customs - Declaration form. When the authorties in SA were doing their inspection did they want to charge you a fee and or have you fill out any Chilean paperwork?
Both AA and LAN have given me different stories on the their procedures. My outfitter has had very few people travel (w/gun) via SA Chile to Cordoba(?).
What I'm most concerned about is on the way down. AA wont transfer my bag to LAN. I believe I will have to go outside of airport control to retrieve my bag and then try to get back into the terminal via Chilean customs with a shotgun in my bag. (gun/foreign country/non-english/eek)