In a large plastic bag combine lime juice, zest, garlic, chili powder, honey, olive oil, cilantro, and jalapeño. Add drumsticks, and toss to coat. Marinate for 30 minutes to 4 hours.
Heat grill to high. Add chicken and cook for 10-15 minutes per side, or until cooked through. Reduce the heat once the chicken is browned, so you can get it cooked through without burning.