Opie invites Andy and Barney to join a club called The Tomahawks. The club is a big boost for the sheriff and his deputy because they've just recently missed out on their chance to join The Esquire Club in Raleigh ("The Clubmen", Episode #42).
The Tomahawks have the following oath, which must be spoken while facing the rising sun:
"As a Tomahawk, I solemnly swear to be fair and square at all times."