Preheat Oven to 400 Degrees
Rinse the chicken and pat dry. Place on a clean cutting board and cover with plastic wrap. Using a meat mallet, pound the chicken breasts out until around 1 inch thick. The purpose is to flatten the meat for more even cooking. Season the chicken with salt pepper; rub with olive oil. Place the meat on a sheet pan and into the oven. Roast for 15 to 18 minutes or until juices run clear when pierced with the tip of a sharp knife in the thickest part.
Remove the meat from the oven and let cool slightly. Place the cooked chicken on a clean cutting board and cut into bit-size pieces
Place the chicken in a large mixing bowl, and add all the ingredients, except basil, and mix well. Season the salad with salt and pepper and mix in the fresh basil and dill.
The chicken salad should be chilled until ready to serve.