Melt the cheeses: Reduce the heat to low. Add the cubed Velveeta and softened cream cheese to the skillet. Stir constantly until the cheeses are fully melted and the mixture is smooth.
Combine the ingredients: Stir in the sour cream, undrained diced tomatoes with green chilies, Worcestershire sauce, garlic powder, and onion powder. Continue stirring over low heat until everything is combined and heated through.
Garnish and serve: Remove from heat and stir in the fresh chives. Transfer to a serving bowl and serve immediately with chips, crackers, or vegetables.
Notes
If you have leftovers, store in an airtight container in the refrigerator for up to 3 days. Reheat in the microwave or stovetop, adding a splash of milk if necessary.