In large bowl or plastic bag, make marinade for chicken by combining 2 tablespoons olive oil, soy sauce, red wine vinegar, Italian seasoning, salt and pepper. Add chicken tenders and marinate in refrigerator for at least 1/2 hour, up to overnight.
In separate bowl, toss apple wedges and onion slices with 1 tablespoon olive oil.
Heat griddle on stovetop on medium. Remove chicken from marinade and dispose of remaining marinade. Grill apples and onions at one end of griddle, and chicken at other.
To prevent apples from burning, flip often and cook until golden brown and tender, about 5 minutes. Grill chicken about 4 minutes on each side, or until chicken is tender and cooked all the way through. Cut into 1-inch pieces. Place chicken, apples and onions in large bowl. Mix and blend dressing ingredients in small bowl. or use your favorite store-bought dressing.Cut romaine heads in half lengthwise and cut off about 1 inch of green leafy end. Salt and pepper lettuce; then, drizzle with olive oil. With the lengthwise cut side down, grill on griddle until it starts to brown and wilt, about 3 minutes.