Place chicken in a baking dish. Squeeze 1/2 of the lime over the chicken. Drizzle chicken with olive oil. Sprinkle on a little salt and 1 tsp of the cumin. Bake at 350 until cooked fully through (time will depend on size and cut of chicken). Remove from oven and let cool.
While the chicken is cooking, cook the pasta in salted water until al dente. Drain and place in a large tupperware. Drizzle with a little olive oil (to prevent it from sticking) and toss to coat. Place in refrigerator to cool.
Also while the chicken is cooking, heat a large skillet over medium heat. Add 1/2 Tbsp olive oil to the pan. Sautee the onion and bell pepper until soft, approximately 5 minutes. Remove from heat and let cool to room temperature.
In a small bowl, make the sauce. Mix together the mayonnaise, sour cream, cilantro, chili powder, the other 1/2 of the lime juiced, 1/2 tsp cumin, and a pinch of salt and pepper. Stir to combine and season to taste.
Cut or shred the chicken into bite sized pieces.
In the large tupperware or a large bowl, combine the chicken pieces, chilled pasta, onion and pepper mixture, and the sauce. Toss to coat. Depending on the shape of the pasta, you may need to add more sauce to get the consistency you want as shapes with more edges and holes will require more sauce.
Chill until ready to serve.