Heat oil in a large nonstick skillet over medium-high. Add chicken; cook until golden brown on bottom, 3 to 4 minutes. Flip chicken, and cook until golden brown, 2 to 3 minutes. Remove from pan. Sprinkle with salt.
Whisk together mayonnaise, juice, sugar, and pepper in a large bowl. Add arugula, onion, celery, and capers; toss gently to coat. Divide among 4 plates; serve with chicken. Top with chives.