Preheat a grill or grill pan to medium-high heat. Drizzle chicken with 1 Tbsp. olive oil. Season the chicken with salt and pepper to taste. Place chicken on the grill and cook for 5-6 minutes per side or until done. Set aside. Once cool, cut into bite size pieces.
Cook the pasta in boiling salted water according to package directions; drain.
Place pasta, chicken, tomatoes, olives, red peppers and spinach in a large bowl. Drizzle with olive oil and season with salt and pepper to taste.