In a skillet, brown the chicken in the oil for about 5 minutes per side or until cooked through. Season with salt and pepper. Set aside on a plate and let cool. Cover with plastic wrap and refrigerate until completely chilled. Slice thinly. Set aside.
In a bowl, combine all the ingredients. Season with salt and pepper.
In a large bowl, combine the lettuce, avocado, bell pepper and onions. Divide the salad among four plates. Top with chicken slices and drizzle with the dressing. Season with pepper.
You can also grill the chicken and serve it hot on the salad.