Grilled Jerk Chicken Drumsticks

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1 habanero or Scotch Bonnet chile pepper, cut into 6 to 8 pieces

3 scallions, roughly chopped

10 fresh thyme sprigs

1/4 cup vegetable oil, plus more for the grill

2 tablespoons packed light brown sugar

2 tablespoons distilled white vinegar

1/2 teaspoon ground allspice

1/2 teaspoon ground cloves

Kosher salt and freshly ground pepper

8 skinless chicken drumsticks (about 2 pounds)

Lime wedges, for serving