In a medium bowl, whisk together the balsamic vinegar, tamari, apple cider vinegar, olive oil, oregano, black pepper, salt, garlic, and 1 tablespoon honey.
Add the chicken thighs and coat well. Cover and refrigerate for at least 1 hour or up to 8 hours.
Remove the chicken from the refrigerator 30 minutes before cooking. Remove the chicken from the marinade, pat dry lightly, and reserve the marinade.
For outdoor grilling, preheat the grill with direct and indirect heat zones. Grill the chicken skin side-down over medium-high heat for 2 to 3 minutes per side.
Move the chicken to indirect heat and cook for 25 to 30 minutes until the internal temperature reaches 185°F.
For the indoor method, preheat the oven to 400°F. Sear the chicken in a grill pan over medium-high heat for 2 to 3 minutes per side.
Transfer the chicken to a baking dish and roast for 20 to 30 minutes until the internal temperature reaches 185°F.
Simmer the reserved marinade with the remaining 2 tablespoons honey over medium heat until thickened into a glaze.
Rest the chicken for 5 minutes, then brush with the balsamic glaze before serving.