Place diced chicken, fajita seasoning, and vegetable oil in a plastic bag and allow to marinate for at least an hour. (Overnight marinating is best though.)
Sauté chicken in a skillet until cooked thoroughly.
Add peppers and onions to the skillet and cook until tender and the onions are translucent.
Place chicken and pepper mixture into a food processor or blender.
Top the chicken mixture with cubed cream cheese and pulse until well-combined.
Add shredded cheddar jack cheese and pulse once again until well-combined.
Spread cheese mixture into an oven-safe dish or cast iron skillet and bake for 20 minutes, or until cheese is bubbly and melted.
Serve warm on a trivet with tortilla chips for dipping.