Let chicken stand at room temperature 45 min.
Preheat oven to 375°F.
Rinse chicken inside and out with cold water; pat dry with paper towels.
Trim off and discard excess fat.
Season chicken inside and out with salt and pepper.
Place 4 thyme sprigs in body cavity.
Place chicken in an oval roaster.
Scatter garlic, carrots and remaining 4 thyme sprigs around chicken.
Drizzle chicken and vegetables with olive oil.
Cover and roast 1 hr.
Uncover pan and preheat broiler.
Broil chicken 4" from heat source until skin is golden and an instant-read thermometer inserted into thickest part of thigh, away from bone, registers 170°F, 10-15 min.
Transfer chicken and carrots to a warmed platter (leave garlic in pan), cover loosely with foil and let rest 15 min.
Remove thyme sprigs from pan and skim fat from pan drippings.
Add stock, bring to a boil over medium-high heat and cook, stirring to scrape up any browned bits from the pan bottom.
Puree mixture with a blender or stick blender until smooth.
Add vinegar and season with salt and pepper.
Carve chicken and pass sauce alongside.