Place the jalapeño pepper, rice vinegar, olive oil, soy sauce, lime juice, honey, dried thyme, salt, garlic powder, and allspice in a food processor and blend until smooth.

Pour the marinade into a gallon sized Ziploc bag. Add the chicken pieces to the plastic bag and try to remove as much air as possible. Seal the bag and slosh the marinade around to coat all the chicken pieces.

Let chicken marinate overnight or as long as you can.
Preheat the grill to medium high heat (350-400 degrees F).

Remove the chicken from the marinade and place on the grill.

Grill for 6-10 minutes on each side or until the chicken's internal temperature reaches 165 degrees Fahrenheit. The drumsticks and chicken thighs will cook at different rates because of their size difference, so make sure to check for doneness often.

Plate and serve warm.