Heat the olive oil in a small sauté pan over low heat. Add the onion and cook until caramelized.
Meanwhile, preheat a gas grill or cast-iron grill pan on medium heat. Oil the grates and make sure they are well coated. Season the chicken with salt and pepper, to taste, and grill until the internal temperature reaches 165 degrees, about 6-7 minutes per side. Once cool, dice the chicken.