In a bowl, whisk together coconut milk, lime zest, lime juice, honey, minced garlic, grated ginger, salt, and pepper.
Place the chicken breasts in a large resealable bag or a shallow dish and pour the marinade over them. Seal the bag or cover the dish and refrigerate for at least 1 hour, or overnight for maximum flavor.
Preheat the grill or a large skillet over medium-high heat. Add olive oil to the skillet if using.
Remove the chicken from the marinade, letting the excess marinade drip off. Reserve the marinade for later use.
Grill the chicken for 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C) and the chicken is beautifully golden.
While the chicken cooks, pour the reserved marinade into a saucepan and bring it to a boil over medium heat. Allow it to simmer for about 5 minutes until it thickens slightly.
Once the chicken is done, serve it hot, drizzled with the thickened marinade, and garnish with fresh cilantro and lime wedges on the side.