Paying with a Gold Chain

A traveler must pay an innkeeper one gold link per day for seven days, using a chain of 7 identical links. The innkeeper insists on holding exactly the right number of links each day, but is willing to give change from links already paid (so the traveler can hand over a larger piece and take back smaller ones). The traveler may cut some links open to break the chain into pieces. What is the minimum number of links that must be cut so that a correct payment can be made every day for all seven days?