In a hot skillet, melt the butter with olive oil.
Add the thinly sliced onions and a pinch of salt. Cook over medium-low heat, stirring occasionally, until the onions are soft, golden brown, and caramelized, about 20 to 30 minutes.
Towards the end of cooking, turn off the heat and add the honey, stirring well to incorporate it evenly into the caramelized onions. Adjust the amount of honey according to your desired sweetness.
In a large bowl, combine the sour cream, cream cheese, caramelized onions (including any juices left in the skillet), and a tablespoon of chopped chives.
Season with salt and pepper to taste, and mix well to combine all the ingredients.
Taste and adjust the flavors as needed, adding more salt, pepper, or honey to your liking.
Garnish the dip with additional chives and caramelized onions just before serving.
Serve the dip with your favorite chips, crackers or vegetables.