Remove any excess fat from the chicken. Coat with oil and season. Once the grill is up to temperature grill, cook the chicken, flipping every 2 - 3 minutes. Cook until internal temperature is at least 165° but I prefer my dark meat chicken between 180°-190°.
For the lemon caper aioli
Combine all ingredients and mix to combine. Can be made ahead of time and stored in the fridge for up to 3 days.
For the sandwich construction
Toast the ciabatta rolls. Once cool enough to touch coat both sides with the aioli. Put on a layer of arugula and then the chicken and top with freshly grated parmesan cheese. Then enjoy!