Preheat oven to 400°F. Lightly coat a 9×13 inch baking dish with cooking spray and set aside.
In a medium bowl, mix shredded chicken, drained tomatoes, green chiles, taco seasoning, and 3/4 cup shredded Monterey Jack cheese until thoroughly combined.
In a medium saucepan over medium-low heat, melt unsalted butter. Whisk in all-purpose flour and cook for 1-2 minutes until bubbly. Gradually pour in chicken broth, whisking constantly, and cook until mixture is slightly thickened and reaches a gentle boil. Remove from heat and stir in sour cream until the sauce is smooth.
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