In a mixing bowl, whisk together the coconut milk, lime zest, lime juice, honey, minced garlic, ground ginger, salt, and black pepper until smooth and well combined.
Place the chicken breasts in a large zip-top bag or shallow dish and pour half of the coconut lime marinade over the chicken. Seal the bag or cover the dish and marinate in the refrigerator for at least 1 hour (or overnight for more flavor).
Preheat your grill or a skillet over medium heat and add the olive oil.
Remove the chicken from the marinade and discard the used marinade. Grill or pan-sear the chicken for about 6-7 minutes on each side, or until the chicken is cooked through and has nice grill marks (internal temperature should reach 165°F).
While the chicken cooks, transfer the remaining marinade to a saucepan and bring to a simmer over medium heat. Allow it to cook for about 5-7 minutes until slightly thickened.
Once the chicken is cooked, drizzle the thickened sauce over the chicken.
Garnish with fresh chopped cilantro.
Notes
Serve with lime wedges and cilantro, alongside jasmine rice.