Heat oven to 425 degrees. Heat oil in ovenproof skillet over high heat. Season chicken with salt and pepper. Cook in skillet, skin-side down, until brown, 3 to 4 minutes. Flip; cook 1 minute. Remove chicken; add vegetables. Reduce heat to medium low; cook 5 to 6 minutes.
Add wine, and bring to boil. Stir in the herbs, capers, and tuna; add the chicken. Transfer skillet to oven, and roast until chicken is cooked through, about 15 minutes. Remove chicken; transfer to cutting board.
Discard herbs. Let tuna cool; puree until smooth. Add mayonnaise and juice. Slice chicken; arrange over arugula. Top with chilled sauce