Heat the butter and olive oil in a large skillet over medium-low heat. Add the sliced onions and cook for 30-35 minutes, stirring occasionally, until they are soft, golden brown, and caramelized. Let them cool for about 10 minutes.
In a large mixing bowl, combine the softened cream cheese, sour cream, mayonnaise, Worcestershire sauce, minced garlic, salt, and black pepper until smooth.
Fold the cooled caramelized onions and chopped chives into the creamy mixture until evenly combined.
Cover and refrigerate for at least 30 minutes to allow the flavors to develop.
Garnish with extra chives and serve with potato chips, crackers, toasted baguette slices, or fresh vegetables.