For the chicken:
1 (3- to 4-pound) whole chicken
3 tablespoons creamy Caesar dressing
1 tablespoon olive oil
1/2 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
4 medium romaine lettuce hearts, chopped
For the dressing:
2 tablespoons lemon juice
1 clove garlic, minced
2 teaspoons anchovy paste
1 teaspoon Dijon mustard
1/4 cup shaved Parmesan cheese
1 cup croutons
Arrange a rack in the middle of the oven and heat to 400°F.
Remove the giblets from the cavity of the chicken. Pat the chicken dry with paper towels. Blot inside the body cavity as well, getting the chicken as dry as you can, inside and out. Use your fingers to gently lift the skin away from the flesh of the chicken, around the breasts and legs. Rub 2 tablespoons of the dressing under the skin, then rub the remaining 1 tablespoon inside the cavity. Rub the oil all over the outside of the chicken, then sprinkle with the salt and pepper.
Place the romaine in an even layer in a roasting pan. Place a roasting rack on top of the lettuce, then place the chicken, breast-side up, on the rack. Roast until a thermometer inserted into the thickest part of the thigh not touching bone registers 165°F, about 50 to 60 minutes.
Transfer the chicken to a cutting board and let it rest for 15 minutes. Meanwhile, remove the roasting rack, then use tongs to transfer the lettuce to a large bowl; set aside. Pour the drippings from the pan into a separate medium bowl. Add the lemon juice, garlic, anchovy paste, and Dijon mustard, and whisk to combine; set aside.
Carve the chicken: Use a sharp knife to cut away the wings and the legs from the chicken. Cut the legs at the middle joint to separate the drumsticks and thighs. Carve off the chicken breasts and cut crosswise into thick slices.
Add the dressing to the lettuce and toss to combine. Transfer to a platter or large plate. Top with the Parmesan cheese and croutons. Arrange the chicken pieces on top of the salad and serve warm.