Heat oven to 375°F. In 10-inch skillet, heat olive and chili oil over medium-high heat. Add chicken; cook and stir 2 to 3 minutes or until lightly browned and no longer pink in center. Reserve several bell pepper strips of each color for garnish; add remaining strips to skillet. Cook about 1 minute, stirring frequently, until slightly softened. Sprinkle with garlic salt, cinnamon, chili powder, black pepper, ground red pepper and lime juice; stir to mix. Remove from heat; cool slightly.
In large bowl, beat eggs, whipping cream, salt and green chiles with wire whisk until blended. Gently stir in both cheeses. Stir chicken mixture into egg mixture.
Place pie crust in 10-inch quiche dish or 9-inch glass pie plate as directed on box for One-Crust Filled Pie. Pour chicken mixture into crust-lined pan. Arrange reserved bell pepper strips in pinwheel fashion over filling.
Bake 35 to 45 minutes or until knife inserted in center comes out clean and filling is golden brown. Let stand 15 to 20 minutes on wire rack before serving. Serve salsa over individual servings.