1) Heat a griddle pan over medium-high heat.
2) Remove the tenderloins from the chicken breast and set aside for another use. Brush the chicken lightly with oil, then season the skin with salt and pepper.
3) Place the chicken on the griddle skin-side down, and cook until the edges turn opaque, about 6 minutes. (To get nifty cross-hatch griddle marks, about half way through cooking reposition the breast about 45 degrees from their original position.) Season with salt and pepper, and turn chicken over, and cook until firm to the touch, about 6 more minutes.
4) While the chicken cooks, make the gremolata. Chop the garlic, add the salt, and continue chopping to make a paste.
5) In a small bowl, stir the garlic paste together with the lemon zest, parsley and olive oil Season with freshly ground black pepper, to taste.
6) Slice the breasts, against the grain and serve with the gremolata.