Prepare the chicken breasts by marinating them in lime juice, olive oil, salt, and pepper for at least 30 minutes.
Preheat the grill to medium-high heat, ensuring it is properly oiled.
Grill the marinated chicken for approximately 6-7 minutes on each side or until fully cooked through.
While the chicken is grilling, prepare the salad ingredients by chopping the vegetables and placing them in a large bowl.
Remove the chicken from the grill and let it rest for a few minutes before slicing it thinly.
Add the sliced chicken to the bowl of salad ingredients, tossing to combine.
In a small bowl, whisk together lime juice, olive oil, salt, and pepper to make the dressing.
Drizzle the dressing over the salad and toss gently to coat all ingredients evenly.
Serve immediately, garnished with additional cilantro if desired.