Drill with a 7/16-spade bit two holes the same width apart as the two-seat swing is wide. Drill the holes vertically through an 8-inch-thick branch. Choose a location far enough out on the branch so those in the swing will not hit the trunk but close enough so both holes are in parts of the branch with the same thickness.
Push an eyebolt through each of the holes so the loop on the eyebolt is pointing toward the ground.
Secure the eyebolt in place by putting two washers on the end and screwing a locking nut on top of the washers. Repeat with the remaining eyebolt.
Clip a spring-loaded clip through each of the eyebolt holes.
Insert the end of the chain on the left side of the swing into the spring-loaded clip on the left side of the branch and close the clip to hold the chain in place.
Repeat attaching the chain on the right side of the swing into the remaining clip on the right side of the branch to finish hanging the swing.