A saw chain includes a tie strap adapted to be pivotally connected to other links of the saw chain. The tie strap features an interior hole with a chamfered edge. An interior counterbore in the interior hole receives a barrel portion of a rivet. The rivet has two flanges extending from both sides of the barrel, each with a smaller diameter than the barrel, and each with chamfered corners in a transition area where the flanges meet the barrel. An exterior counterbore on an exterior surface of the tie strap receives a rivet head formed from one of the flanges, such that an exterior surface of the rivet head sits flush with the exterior surface of the tie strap.