In a small bowl stir together the chili sauce, garlic, lime zest and juice, thyme, paprika, and oil. Season with salt and pepper and set the marinade aside.
Place the chicken, breast side up, on a cutting board. Pull back the neck skin to expose the meat at the neck cavity and use your fingers to locate the wishbone at the opening. Using a sharp boning knife, cut just behind the wishbone, working your way down on both sides of the bone until it is fully detached, then pull the bone free of the cavity. Turn the chicken breast side down and, starting at the neck end, cut along first one side of the backbone to the tail end and then the other side of the backbone to the tail end. Lift out the backbone and reserve for stock or discard. Once again turn the chicken breast side up and, using your hands, press against the breastbone until it snaps and the chicken lies relatively flat.
Rub the chicken, skin side only, with the marinade. If you like, make incisions into the flesh with a sharp knife to help the marinade penetrate. Let marinate at room temperature for 2 hours.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Prepare the grill for cooking over medium heat (400°F).
Brush the cooking grates clean. Grill the chicken, skin side down, over direct medium heat , with the lid closed but watching for flare-ups, until the skin releases easily from the grates and is golden, 5 to 10 minutes.
Brush the cooking grates clean. Grill the chicken, skin side down, over medium heat , with the lid closed but watching for flare-ups, until the skin releases easily from the grates and is golden, 5 to 10 minutes.
Using tongs and a large spatula, turn the chicken over and continue to grill with the lid closed until an instant-read thermometer inserted into the thickest part of the chicken breast registers 165°F, 25 to 35 minutes more.
Remove from the grill, and rest at room temperature, indoors, for 5 to 10 minutes.