Preheat oven to 350 F.
In medium bowl, whisk eggs. Season with salt and pepper. Add ricotta cheese and stir, leaving cheese in small chunks.
In 12-inch non-stick frying pan, melt butter over medium heat. Add shallots and sauté 4 – 5 minutes until softened. Add red peppers and sauté 4 minutes. Add one half of arugula and cook to wilt, turning with tongs. Add remaining arugula and wilt in same manner. Stir in chicken to combine with vegetables.
Pour egg mixture into pan with vegetables and chicken. Sprinkle with Parmesan cheese. Cook over medium heat for about 10 minutes, or until edges of frittata are set.
Place pan in oven and bake for 20 minutes. Remove frittata and allow to rest for 5 minutes before slicing and serving.