You find the chair on the level "The Estate"
This one is somewhat confusing by name. The "rocking chair" is actually more similar to a porch/patio swing. There are two swing sets shortly after you play the eating minigame. Soften an enemy up quite a bit because the swing BARELY does any damage. You don't have to be the one to hit the swing as I had an enemy punch the swing and eliminate another enemy and it unlocked for me. Consider plugging in a second controller as the AI sometimes gets in the way and knocks out enemies before you can eliminate them with the swing.