Turn on broiler to high. Place bell peppers under broiler and broil from 5 minutes on each side until skin blisters and begins to turn black.
Remove peppers from oven, set aside. Preheat oven to 350 degrees.
In a medium size mixing bowl combine the shredded chicken with 1 cup shredded cheese, the pesto and the quinoa and toss to coat.
Once peppers are cool enough to handle, slice in half and remove membranes and seeds. Add a heaping 1/4 cup of the chicken mixture to each pepper and top with cheese.
Bake for 10 minutes. Serve immediately.