Position a rack in the middle of the oven and preheat the oven to 400°F. Line a roasting pan with aluminum foil. Place a v-rack in the roasting pan and set the pan aside.
Rinse the chicken inside and out and pat it dry. Place the marmalade on a cutting board and chop it briefly to break up any large pieces. In a small bowl, use a fork to mix the marmalade, coarse sea salt, rosemary, and butter together into a paste. Carefully work your fingers under the chicken’s skin to loosen it from the flesh. Start from the neck and try not to tear the skin. Gently work the butter mixture under the skin with your fingers, spreading it as evenly as possible all over the bird.
Brush the outside of the chicken all over with the olive oil, then sprinkle it liberally outside and in with kosher salt and pepper. Stuff the lemon quarters and rosemary sprigs into the cavity, packing them as tightly as possible. Roughly truss the chicken by tying the legs together at the neck end with kitchen twine.
Place the chicken breast side up in the prepared pan and roast for 20 minutes. Turn the chicken breast side down and roast it for a further 20 minutes. Turn it breast side up again and continue roasting until it is just cooked and the juices run clear when you pierce the thigh joint with a skewer, about another 20 minutes. As soon as the chicken is fully cooked, turn it breast side down and prop it against the side of the pan at a 45-degree angle with the legs up so that the juices run into the breast. Tent the chicken with aluminum foil and let it rest for 10 minutes.
To serve, remove the lemon quarters from the cavity, carve the chicken, and squeeze the lemony juices over the carved meat.