We can cut one link near the middle to make a chain of 4 links, a chain of 2 links and the cut link itself.

Day 1, we give him the cut link

Day 2, we take back the cut link, give him the 2 link chain

Day 3, we give him the cut link

Day 4, we take back both the cut link and the 2 link chain, give him the 4 link chain

Day 5, we give him the cut link

Day 6, we take back the cut link, give him the 2 link chain

Day 7, we give him the cut link