Preheat a cast-iron grill pan to medium high heat.
Season the chicken breasts with salt and pepper. Place seasoned chicken on the grill pan and cook 3-4 minutes. Flip and cook until the juices run clear.
Set aside to cool slightly, then slice the chicken into 1/4 inch thick strips.
Prepare the salad and salad dressing. In a small bowl, whisk the balsamic vinegar with the oil (reserving 1 tsp. for later) and mustard to emulsify. Season with salt and pepper.
Place the arugula in a medium bowl and drizzle with 1 tsp. oil. Gently massage to coat the leaves, then sprinkle with a small amount of sea salt. Toss in the shredded carrots and olives. Top with chicken and drizzle with dressing and chopped pecans.