For vinaigrette: Combine all vinaigrette ingredients in a bottle or a bowl. Shake or whisk to combine. Set aside.

For chicken: In a bowl, mix butter, oatmeal, pine nuts, onion, garlic, salt, and pepper. Set aside.

Lay chicken breasts on their sides and, with a small paring knife, slice through each, making a pocket. Do not cut through the bottom or top of the breast. Stuff each pocket with oatmeal mixture. Wrap each breast with string, stretching the chicken skin over the pocket opening to hold the stuffing in place. Tie to secure. Season with salt and pepper.

In a skillet over medium-high heat, warm the oil. Add chicken, skin side down. Cover pan and cook for 10 to 12 minutes. Turn breasts over, cover pan, and cook for 10 minutes more. Chicken is done when it is pierced and the juices run clear. Remove chicken from skillet and place on a platter. Remove string. Immediately drizzle with herb vinaigrette, reserving some to pass at the table.