Preheat a covered grill to medium heat (about 375F).
When the grill is hot, brush the grill grate thoroughly with a wire brush until it is clean, and put the salt bricks on the grate.
Cover the grill and heat the bricks while you split the chicken.
Remove and discard any giblets from the cavity of the chicken.
Place the chicken, breast side down, on a cutting board.
With a large knife, cut through the skin down the length of the spine.
This may sound gruesome, but unless you have a heavy cleaver and pinpoint aim to cleave longitudinally through the spine in a single masterful stroke, use the pointy tip of a sturdy chefs knife to pierce the spine several times down its length, sewing machine style, in order to weaken it.
Now you can split the spine in two by lining up the edge of the chefs knife blade with the perforations you just made, and pressing down until the chicken splits into two symmetrical halves
Wash the halves in cold water and pat dry with paper towels.
Coat them with the olive oil and rub them all over with the cut sides of the garlic cloves.
If you want, you can tuck the pieces of garlic under the edges of the skin.
Put the chicken halves, skin side down, on the grill grate and, using grill gloves or thick oven mitts (or sturdy tongs, if you have them), put a hot salt block on top of each half.
Close the grill and cook until the chicken skin is crisp and deeply grill marked, about 20 minutes.
Remove the blocks using the grill gloves, flip the chicken halves with tongs, put the bricks back on top of the chicken, close the grill, and cook until an instant-read thermometer inserted into the inside of the thickest part of the thighs registers 160F, 10 to 15 minutes.
Remove the salt bricks, transfer the chicken to a clean cutting board, and allow it to rest for 5 minutes (the internal temperature should reach 165F) before cutting it into parts and serving.