Prepare a grill for medium-high heat. Brush the grill with olive oil to coat.
Put the chicken in a resealable plastic bag. Crush the peppercorns in a mortar and pestle and tip into a bowl. Add the salt and garlic and mix. Add the mixture to the bag with the chicken and drizzle over the olive oil. Seal the bag and shake to coat the chicken.
Grill the drumsticks, turning every 5 to 7 minutes, until cooked through, 30 to 35 minutes. Serve with BBQ sauce if desired.