In 3-quart saucepan, place potatoes, leek, garlic, salt and broth. Cover and heat to boiling; reduce heat. Simmer covered 20 to 25 minutes or until tender (do not drain). Mash potato mixture with potato masher or electric mixer on low speed.
In 1-quart saucepan, heat 1/4 cup whipping cream and the butter over medium heat, stirring occasionally, until butter is melted. Add cream mixture to potato mixture; continue mashing until potatoes are light and fluffy. Add additional heated whipping cream for desired consistency. Stir in chives.