Prepare your grill for cooking. If using a gas grill, preheat until grill temp measures 400 degrees. If using a charcoal grill, light coals and heat until coals have started to turn grey. Pour evenly over grill bottom for even grilling.
While the grill is heating, place the chicken breasts between 2 large layers of waxed paper. Pound the chicken with a meat pounder until each one is 1/2 inch thick. You may need to pound chicken in batches. Place chicken on platter and brush olive oil on both sides. Using 1 teaspoon of salt and 1/2 teaspoon pepper, sprinkle on both side of chicken. Set aside.
Place pineapple, red onion, remaining salt and pepper in a bowl and combine. Set aside.
If grilling chicken on a stove, rub 1 tablespoon of olive oil on the grilling surface. Preheat grill pan over a high flame until the oil is almost smoking. Cook as directed for a grill. See next step.
Grill pounded chicken breasts 3 minutes on one side. Flip over and grill for another 2 minutes on the second side. With an instant read thermometer, make sure chicken registers 160 degrees. Take off grill.
When ready to plate, place chicken on a plate. Add pineapple salsa on top of chicken, and add arugula next to chicken.
Serve within 15 minutes.