In 10-inch nonstick skillet, heat oil over medium heat. Add onion; cook 4 to 6 minutes, stirring occasionally, until onion is tender. Add garlic; cook about 1 minute or until garlic is fragrant. Stir in chicken, taco seasoning mix, water, tomatoes and green chiles until well coated.
Heat to simmering; cook uncovered 4 to 5 minutes, stirring frequently, until chicken is heated through.
Remove from heat; stir in pepper Jack cheese. Pour mixture into baking dish. Sprinkle with Cheddar cheese.
Bake 20 to 25 minutes or until bubbly around edges and cheese is melted. Top with green onions; serve with chips.