Heat the oil in a large skillet over medium heat. Add the onions and thyme and cook, stirring occasionally, until the onions are very soft and brown, about 20 minutes, reducing the heat to medium-low if the onions brown too quickly. Set aside to cool to room temperature.
Meanwhile, stir together the sour cream, mayonnaise and Worcestershire sauce and season with salt and pepper. Add the onion mixture and stir until well combined. Cover and chill for at least 1 hour or up to overnight. The dip can be made up to 3 days ahead and refrigerated in an airtight container. When ready to serve, scatter the chives over the top and serve with potato chips.
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