Heat the olive oil in a 10-inch skillet over medium high heat. Add the chicken in a single layer and cook 3 minutes, stir the pieces and continue cooking until the chicken is cooked through, about 2 minutes more. Transfer to a bowl and cover to keep warm.
Sauce:
In the same skillet, reduce the heat to medium-low and add the cream cheese. Stir until the cream cheese is melted.
Once melted, stir in the dressing mix until smooth. Slowly add the chicken broth and red peppers, continuing to stir until smooth. Simmer for 3 to 4 minutes to blend the flavors and thicken slightly. Remove from heat and whisk in parmesan cheese.
Add the chicken along with any juices and let rest 3 minutes or until heated through.
Serve over pasta if desired.
Notes
Leftovers will keep in the refrigerator for 3 days and in the freezer for 1 month.