I haven't done it but I emailed US Customs and received the following. BTW you will need Canadian Paperwork from Foreign Affairs for your rifle and scope. I decided that it was less grief to rent a rifle.
Discussion Thread
Response Via Email (Mark) 02/03/2014 04:54 PM
Dear Brian,
You will be OK if you transit the US, and the firearm is in your checked bags. You do not need a permit. You will probably be pre-cleared by CBP officers in Ottawa when you go to South Africa, and they will check the information. On the return journey you need to claim your bags in Atlanta, go through CBP, and then re-check for the flight to Canada. I hope this helps.
Mark
CBP ports:
Locate a Port of Entry | U.S. Customs and Border Protection
CBP pre-clearance locations
http://www.cbp.gov/xp/cgov/toolbox/contacts/preclearance/preclear_locations.xml
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Customer By Web Form 01/28/2014 11:22 AM
Hi,
I will be leaving Ottawa Canada on a hunting trip in South Africa.
Ottawa --> Detroit --> Atlanta --> South Africa and the reverse on the way home. My rifle will be checked through in Ottawa. Your website states "You must be in physical possession of your firearm" not possible on an aircraft. What paperwork if any do you require from me?
Thanks much