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Lateral Thinking #07- Cutting Links -

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Puzzle Image A jeweler is asked to join four small 3-link chains (shown on the left) into a large circular 12-link chain. In order to join two closed links, one of the links needs to be cut, placed onto the other link, and then closed.

The clever jeweler finds a creative way to make the circular chain while cutting as few links as possible. How many links does he cut and what does he do?
Do you have a suggestion for this puzzle (e.g. something that should be mentioned/clarified in the question or solution, bug, typo, etc.)?