Fill a large stock pot with water and bring to a boil.
Add chicken and boil for about 15 to 20 minutes or until chicken is cooked through; chicken should turn white when finished cooking.
In a large skillet, over medium heat, heat 1 tablespoon butter, or olive oil.
Once heated, add chopped onion to skillet and cook until translucent.
Once the onions are translucent, add in the green chilies; cook for about 6 minutes, stirring occasionally.
While the onions and chilies are cooking together, chop the chicken into bite-size pieces.
After the onions and chilies have cooked for about 6 minutes, add in the cream cheese.
Stir the cream cheese into the onions and chilies; continue to stir until the cream cheese has melted.
Once the cream cheese has completely melted, add in the chopped chicken.
Stir everything together until completely combined.
Cook, while stirring every so often, for 5 minutes; remove from heat; set aside.
Pre-heat the oven to 350°F.