Preheat your smoker to 225°F (107°C). In a small bowl, mix together the chili powder, garlic powder, salt, and pepper. Pat the chicken breasts dry and season them evenly on all sides with the spice mixture.
Place the seasoned chicken directly on the smoker grates. Cook for about 1.5 to 2 hours, or until the internal temperature reaches 165°F (74°C) on an instant-read thermometer.
Remove the chicken from the smoker and let it rest for 5-10 minutes. Once cool enough to handle, chop or shred the chicken into bite-sized pieces.
In a 10-inch or 12-inch cast iron skillet, combine the chopped chicken, cubed Velveeta, shredded Pepper Jack, cubed cream cheese, the entire can of diced tomatoes with green chiles (with liquid), diced jalapeno (if using), and milk.
Place the skillet in the smoker. Cook for 60-90 minutes, stirring well after the first 45 minutes to combine the melting ingredients.
The dip is ready when all the cheese has melted and the mixture is hot and bubbly throughout. Stir one last time before serving.
Serve warm with tortilla chips or other dippers.