Sprinkle chicken with salt and pepper. Lightly smash garlic cloves just to flatten slightly, leaving peel attached and cloves as whole as possible.
Heat 4 tablespoons extra-virgin olive oil in heavy large pot over medium-high heat. Working in 2 batches, add chicken and cook until brown on all sides, about 12 minutes per batch.
Transfer chicken to plate.
Add remaining 2 tablespoons olive oil and garlic to pot. Stir until golden brown, about 4 minutes.
Add wine and thyme; bring to boil. Return chicken to pot. Reduce heat to medium, cover, and simmer until chicken is cooked through, moving chicken pieces from top to bottom every 5 minutes (sauce will not cover chicken), about 20 minutes. Season to taste with salt and pepper.
Transfer chicken to platter. Spoon garlic cloves around chicken and drizzle sauce over.