Heat oil in a large nonstick skillet over medium heat until hot. Add onion and saute until it just starts to brown, about 2 minutes. Reduce heat to low, cover, and cook for minutes, stirring occasionally, until golden brown. Remove from heat and let cool for 10 minutes.
Mix mayonnaise, sour cream, cheddar, Tabasco, and salt together in a medium bowl. Add onion and mix until evenly distributed. Spread dip into a shallow 5x7 baking dish and bake until bubbling and slightly browned, about 20 minutes. Stir in chives and serve.