Preheat oven to 350°F. Lightly grease a 9x13 casserole dish and set aside.

In a large mixing bowl, combine shredded chicken, taco seasoning, sour cream, cheddar cheese, and green chilies. Mix thoroughly until all ingredients are evenly distributed and the chicken is well coated. Set aside.

Place saucepan over medium-high heat and add cubed Velveeta along with the entire can of diced tomatoes with green chilies. Stir every 30-45 seconds until cheese melts completely and mixture becomes smooth and pourable, about 5-7 minutes total.

Lay tortillas flat on a clean work surface. Warm them in microwave for 15 seconds if cold. Spoon approximately ¾ cup of chicken mixture into the center of each tortilla, spreading it into a 4-inch horizontal line down the middle, leaving 1 inch from edges. Fold in sides, then roll tightly from bottom to top.

Arrange filled enchiladas seam-side down in prepared casserole dish, placing them snugly against each other. Pour warm queso sauce evenly over the top, making sure every enchilada gets a generous coating.

Bake for 20-25 minutes until queso is bubbling vigorously around edges and enchiladas are heated through. The tops should have slightly golden spots. Let rest 3-4 minutes before serving.