Preheat oven to 375 degrees F. Place chicken on a baking sheet; drizzle with olive oil and sprinkle with salt and pepper. Cook the chicken in oven for six to eight minutes.
Then, on a grill pan over medium-high heat, warm 2 tablespoons olive oil. Using tongs, transfer the chicken from the oven to the grill pan and grill until tender and cooked through, about six to eight minutes more.
Once cooked through, place chicken on a cutting board and set aside to cool. In a medium bowl, combine tarragon, cheese, lemon juice, vinegar, and olives and toss together gently. Cube chicken.
Divide arugula between plates and top with chicken, and olive-cheese mixture. Serve immediately.