Heat the oil in a large skillet over medium-high heat. Add the onions and saute until they are translucent and just beginning to lightly brown, about 10 minutes. Reduce the heat to medium-low and continue to cook until the onions are soft, golden brown, and caramelized, about 20 to 25 minutes longer. If the onions start to burn add 1 to 2 tablespoons of water. Stir in the garlic, salt, and pepper and cook until fragrant, about 30 seconds. Remove from heat and let cool.
In a large mixing bowl combine the yogurt and mayonnaise. Stir in the cooled onions, lemon juice, and Worcestershire. Season with more salt and pepper if necessary. Transfer to a serving bowl, cover with plastic wrap, and let chill for at least one hour or up to two days. Serve with vegetables and chips.