Special equipment: butcher's twine
Mix together the spinach and artichoke dip, feta and caraway in a bowl until very smooth and uniform. Transfer the mixture to a piping bag (or use a ziptop bag and cut off the tip to create a 1/2-inch-wide opening).
Lay the breasts on a cutting board. Using a sharp boning knife, cut a pocket in the thickest part of each breast. Gently swipe the knife back and forth without making the hole larger or piercing the underside or top of the chicken.
Pipe some filling into each pocket. Tuck the tip of each breast under and secure with one long piece of butcher twine tied into a cross, making sure to seal the pocket hole with the twine. Sprinkle with salt and pepper. Refrigerate the chicken for 1 hour to firm up.
Prepare a grill for a 2-stage fire (one hot side, one cool side).
Set the chicken on the cool side of the grill top-side down. Cover and cook, flipping and rotating halfway through, until the thickest part of the meat registers 160 degrees F, about 15 minutes. Move to the hot side of the grill and cook until both sides are charred, 2 to 3 minutes a side.
Transfer the chicken to a cutting board, loosely tent with foil and let rest for 5 minutes. Remove the twine and slice into medallions.