In a bowl, combine cream cheese and 1 tbsp dip mix.
Cut each chicken breast in half, crosswise. You should have 4 pieces.
Using the tip of a knife, cut a pocket in the thickest part of each chicken breast. Make sure not to cut all the way through. Using your fingers, widen each hole.
Spoon 1 tbsp cream cheese mixture into each pocket. Fasten with a toothpick to secure, if needed.
In a large, non-stick fry pan, heat oil over medium-high. Add chicken; reduce heat to medium. Cook until deep golden, about 5 min per side.
Meanwhile, slice pepper and onion into thin strips. Add to pan; sprinkle with remaining 1⁄2 tsp dip mix and stir in water. Cover; simmer until peppers are tender, 2–4 min.
Place chicken on plates and top with peppers and onion (and any juices in pan). Remove toothpicks before serving.