Season chicken breasts with salt and pepper. Heat oil in a skillet over medium-high heat and cook chicken for about 6 minutes per side until fully cooked through. Allow to rest before slicing.
While chicken cools, chop bell peppers, julienne carrots, and dice cucumbers.
In a bowl, whisk together peanut butter, soy sauce, lime juice, and water until smooth. Adjust water for desired consistency.
Once the chicken has cooled, slice it into strips or cubes. In a large bowl, combine chicken with chopped veggies and herbs.
Drizzle peanut dressing over the salad mixture and toss gently to combine.