Heat 1 teaspoon oil in a Dutch oven over medium-high heat. Add chicken, and sauté 3 minutes. Remove from pan; set aside.
Heat 2 teaspoons oil in pan. Add apple and next 4 ingredients (apple through bell pepper); sauté 5 minutes, stirring frequently. Stir in the flour and next 4 ingredients (flour through salt); cook 1 minute. Stir in broth, chutney, and tomato paste; bring to a boil.
Reduce heat; simmer 8 minutes. Return chicken to pan; cook 2 minutes or until mixture is thoroughly heated. Sprinkle with parsley, if desired.