1) Preheat oven to 375 degrees F. Cube chicken, grate cheese, and mince jalapenos and garlic.
2) In a 12-inch oven-safe skillet, add a drizzle of oil and chicken over medium. Season chicken with salt and pepper and cook until the chicken is cooked through, 6-8 minutes. Then remove chicken and chop finer or shred.
3) Return chopped chicken to skillet with jalapeno and garlic. Cook for a minute or two. If skillet is really dry, add a drizzle of extra oil.
4) Add flour and stir into the mixture, then stir in milk in a slow stream. When milk is stirred in, add buffalo sauce and stir to combine. Cook the mixture over medium heat until hot and it is the consistency of a gravy.
5) Add grated monterey jack cheese and stir to melt. Then add cheddar on top. Season the dip with salt and pepper.
6) Bake dip until bubbly and slightly browned around the edges, 18-20 minutes. If you want it more browned, you can broil the dip for a minute at the end, but make sure your skillet is broiler-safe.
7) Remove dip from oven and garnish with chives and a drizzle of extra buffalo sauce. Serve while warm with tortilla chips.