Preheat oven to 350°. In a large bowl, stir together cream cheese, shredded chicken, black beans, 1 cup pepper jack, 1 cup cheddar, enchilada sauce, green chiles, and taco seasoning.
Transfer dip to an ovenproof skillet and top with remaining 1/2 cup cheeses. Bake until warmed through and bubbly, 20 to 25 minutes.
Garnish dip with cilantro and serve with tortilla chips.