Place water in a large pot over high heat and bring to a boil.
Stir in the salt and brown sugar until dissolved. Remove from heat and let cool completely.
Add vinegar, pickling spice, black pepper, allspice, garlic powder, and tarragon and mix well.
Transfer brine to a large resealable container (or keep it in the pot if you have a tight-fitting lid).
Add the chicken. Make sure it's fully submerged. Add more water if it's not.
Cover and refrigerate for 4-8 hours.
Fire up your grill for direct heat cooking with a rotisserie.
Remove the chicken from the brine and and shake off any excess.
Pat try and sprinkle generously with pepper. Transfer to a rotisserie basket (you might have to work in batches) and put onto the grill.
Grill until the internal temperature reaches 165 F. Mine took about 20 minutes. Cook time will depend on the heat and how thick your chicken breasts are.
Notes
You can also cook the chicken directly on your grill grates over medium-high heat.