In a medium bowl, whisk together the coconut milk, lime zest, lime juice, honey, minced garlic, grated ginger, salt, and black pepper until well combined.
Place the chicken breasts in a large resealable plastic bag or shallow dish and pour the marinade over the chicken. Seal the bag or cover the dish and refrigerate for at least 1 hour, preferably overnight for maximum flavor.
Preheat your grill or stovetop grill pan over medium-high heat. If using a stovetop grill pan, add 2 tablespoons of olive oil to prevent sticking.
Remove the chicken from the marinade, allowing any excess marinade to drip off. Discard the marinade.
Grill the chicken for about 6-7 minutes on each side or until the internal temperature reaches 165°F (75°C). The chicken should have a nice char and be cooked through.
Once cooked, remove the chicken from the grill and let it rest for a few minutes.
Slice the chicken and serve it drizzled with additional lime juice and garnished with fresh cilantro if desired.