Whisk the rum, orange juice, orange zest, Worcestershire sauce, ginger, brown sugar, garlic, and cilantro together in a large bowl. Add the chicken pieces, cover with plastic wrap and refrigerate for at least 30 minutes or up to 4 hours.
Preheat your grill to medium-high heat.
Remove the chicken from the marinade and place the chicken on the grill and cook until browned on both sides and the juices run clear, about 10 minutes per side, basting with leftover marinade a few times throughout. Serve sprinkled with cilantro and garnish with the orange slices.