Pat the chickens dry inside and out with paper towels and season well with the Lemon Thyme Brine or just straight up kosher salt.
Heat a gas or charcoal grill for medium high, indirect heat. At the grill, crack open two of the beers and slowly lower a chicken onto each. Don’t stress if some of the beer spills out in the process. You could also grab yourself a set of these chicken and beer holders for even easier grilling. Set the chickens on the grill over indirect heat and cook for 60 to 75 minutes or until the chicken reaches 165 in the thickest part of the thigh. During the last 5 minutes of grilling, grill the citrus halves over direct heat until charred. Remove the chicken from the grill and rest for at least 15 minutes.
Meanwhile, heat a skillet over medium high heat. Add a teaspoon of oil and the minced shallot and cook until the shallot is tender. Add about 1/3 cup beer to the skillet followed by the juice of the charred citrus. Cook until reduced by half. Remove the pan from the heat and swirl in the butter until the sauce thickens.
Remove the chickens from the cans and carve. Serve the chickens with the citrus beer sauce.