Examine the tree branch where you will hang your chair. The tree branch needs to be healthy and strong enough to hold your weight as well as the weight of the chair.
Buy a chain and two quick links that are able to support your weight. Ask a hardware or building supply store sales associate what size of chain should be able to hold your weight. The length of the chain will depend on the height of your tree and how far you wish the hammock chair to dangle from the ground.
Slip one end of the chain through some thick plastic tubing. When you hang the hammock chair from a tree, the plastic tubing will protect the wood from the tough metal chains. Without the plastic tubing, the chain can start to eat through the tree branch and sever it from the tree.
Set a stepladder under the branch and climb onto it while you hold the chain. Loop the end of the chain with the plastic tubing around the branch. Connect the end of the chain to the other side using one of the quick links, securing the loop in place.
Step off the ladder and connect the second quick link to the dangling end of the chain. Connect the hammock chair's connection loop to the quick link.
Set a weight into the chair to test the stability. If the branch bows dangerously, remove the weight and relocate the hammock chair.