Preheat the oven to 400 degrees F. Then while the oven is preheating, boil the water to cook the pasta.
Slice the red and green bell peppers and then toss with 1 tbsp of olive oil, salt, and pepper to taste in a medium bowl. Add peppers to baking sheet, spreading evenly. Then add salt and pepper to the chicken breast. Cut chicken breast in half or into quarters if it is a large breast so that it cooks through quicker. Add to the same baking sheet next to the peppers or to a separate sheet if you are using smaller baking sheets.
When the pasta is cooked to al dente, drain into a colander, and then rinse with cold water.
Bake chicken for 20-25 minutes or until the chicken is no longer pink and the bell peppers are tender. Shred the chicken after 2 minutes once it has cooled off.
Combine the pasta, chicken, red onion, basil, parsley, and bell pepper in a large bowl. Toss gently. In a small bowl, add 2 tbsp of olive oil and red wine vinegar, 1 tbsp of cold water, salt, black peppers, and minced garlic. Stir with a whisk until mixed thoroughly. Drizzle dressing over the pasta mixture. Toss gently to coat. Serve immediately. Or keep refrigerated until ready to serve. Save dressing in a separate container and add to pasta mixture right before serving.