Place potatoes in a medium saucepan; add water to cover. Bring to a boil; cover, reduce heat, and simmer 20 minutes or until potatoes are tender. Drain; return potatoes to pan. Mash with a potato masher.
Heat oil in a small nonstick skillet over medium heat. Add onion, and cook 3 minutes or until soft; stir in milk and cheese. Reduce heat to low; cook 4 to 5 minutes or until heated and cheese begins to melt. Add milk mixture to mashed potatoes. Stir in chives, salt, and pepper.