In a small bowl, mix chile paste, vinegar, rosemary, and oil. Chiarello loves the paste's flavor: "I call it Calabrian ketchup. It's fruity and a little bit smoky, with nuanced heat."
Put chicken in a glass dish just large enough to hold it flat. Add marinade and turn to coat. Marinate 2 hours or chill overnight, turning a few times (bring to room temperature before grilling).
Build a fire and let burn to ashy chunks (see "The DIY Firepit," below). Using tongs, oil hot cooking grate well with a wad of paper towels.
Pat excess marinade off chicken halves and season with 1 1/2 tsp. salt. Arrange halves on grate, skin side up and touching down the middle. Oil bottom of a cast-iron skillet and set on chicken. Add a foil-wrapped brick to skillet.
Cook chicken until crisp and brown underneath, 10 to 13 minutes. If flames flare up, squirt them with water. Turn bird over and cook, still weighted, until brown and crisp and an instant-read thermometer registers 170° when inserted in a thigh, 11 to 13 minutes.
Transfer to a cutting board, cover with foil, and allow to rest 5 minutes. Cut in quarters, season with salt, and serve.
*Find Calabrian chile paste at napastyle.com as "Silafunghi hot chili sauce." Or mix 1 tbsp. minced roasted red peppers with 1/2 tsp. each extra-virgin olive oil and lemon juice and 1/4 tsp. each salt, red chile flakes, and smoked Spanish paprika.
The DIY Firepit
"You can do anything on this. It's a little like camping in the middle of your day," says Napa Valley chef Michael Chiarello. All you need is bricks arranged to fit under your cooking grate and some sand.
Build the pit: Spread a double layer of heavy-duty foil on the ground ("not grass," warns Chiarello, since it may scorch). Make it big enough to extend a foot beyond your cooking grate in all directions. Build a brick rectangle 3 layers high, leaving a couple of bricks out of the top layer on opposite sides, to encourage airflow. (For a standard 21-in. round Weber grate, the rectangle should be 2 bricks by 3 bricks.) Fill with about an inch of sand.
Light the fire: Put several balled-up sheets of newspaper in the center and position kindling into a tipi around it; lean larger kindling and then 5 to 6 small logs (preferably oak). Light the fire. "The tipi lets every bit of flame go up past 3 or 4 logs," says Chiarello, so the fire starts fast. Once the logs have caught, add several larger logs to the perimeter. Let them burn down to ashy chunks with low flames (1 1/2 to 2 hours). Because there's less smoke and char than cooking over a flaming fire, Chiarello says, "it makes your food taste much cleaner, gives nuanced flavor, and is better for wine."
Start cooking: Keep another log burning at the back of the pit. When it's ashy chunks, rake it into the main fire to maintain heat.