Combine olive oil, minced garlic, chopped chipotle peppers, thyme, smoked paprika, salt, and pepper in a mixing bowl to create a flavorful marinade.
Place the chicken drumsticks into the marinade, ensuring each piece is thoroughly coated. Cover and refrigerate for at least 20 minutes to allow the flavors to penetrate.
Preheat your grill to medium-high heat until hot and slightly smoky, aiming for around 375-400°F (190-200°C).
Arrange the marinated drumsticks on the grill grates, skin-side down, and cook for about 5-7 minutes, pressing lightly to promote even browning and crisping.
Flip the drumsticks and cook for another 15-20 minutes, turning every 5 minutes, until the skin is deeply charred in spots and the internal temperature reaches 165°F (74°C).
During the last few minutes, move the drumsticks to indirect heat if necessary to prevent burning, allowing the interior to cook through evenly.
Once cooked, remove the chicken from the grill and let rest for 5 minutes, so the juices redistribute and the skin remains crispy.
Serve the drumsticks hot, with the smoky, spicy aroma wafting from the crispy, caramelized exterior, ready to enjoy.