Warm the oil and unsalted butter together in a large heavy skillet over medium heat until the butter melts.
Add the diced onions and ¼ teaspoon salt, stirring to coat.
Reduce heat to medium-low and cook, stirring every few minutes, until the onions turn deep golden brown and sweet, about 30 minutes. Add a splash of water if they begin sticking.
Remove the skillet from heat and let the onions cool for 10 minutes. Transfer to a bowl.
Add black pepper, smoked paprika, garlic powder, the remaining ¼ teaspoon salt, sour cream, mayonnaise, Dijon mustard, and Worcestershire sauce and mix until smooth.
Cover and chill at least 30 minutes to let flavors meld.
Transfer the dip to a serving bowl, sprinkle the chopped fresh chives over the top, and surround with potato chips.