Preheat your oven to 350°F (175°C).

In a large mixing bowl, combine the shredded chicken, taco seasoning, sour cream, shredded cheddar cheese, and chopped green chilies. Mix thoroughly.

In a medium saucepan, melt the cubed Velveeta cheese with the diced tomatoes and green chilies over medium-high heat, stirring frequently.

Spoon ½ to ¾ cup of the chicken filling into the center of each tortilla, roll it tightly, and place it seam-side down in a greased casserole dish.

Pour the smooth queso sauce evenly over the assembled enchiladas.

Bake for 20 to 25 minutes, or until the sauce is bubbling and the top is slightly golden. Let it cool before serving.