Place the potatoes in a large pot and cover with water. Bring to a boil over high heat. Reduce heat to medium-low and cook at a low boil until the potatoes are tender, 10-12 minutes.
While the potatoes boil, melt the butter in a small pot. Add the garlic and cook, stirring, for 1 minute. Add the olive oil, whisk to combine, and remove from heat.
When the potatoes are tender, transfer to a large bowl. Add the butter mixture, 2 tablespoons chives, and salt and pepper, to taste. Mash to reach desired texture. Serve topped with pats of butter and remaining tablespoon of chives sprinkled on top.