In a large bowl, combine coconut milk, olive oil, minced garlic, grated ginger, soy sauce, lime juice, cumin, paprika, salt, and pepper. Whisk until well blended.
Add the chicken breasts to the marinade, ensuring they are fully coated. Cover and refrigerate for at least 30 minutes, or up to 4 hours for more flavor.
Preheat your grill or a skillet over medium-high heat. If using a skillet, add a little olive oil to prevent sticking.
Remove the chicken from the marinade, letting any excess drip off. Discard the marinade.
Grill or cook the chicken for about 6-7 minutes on each side, or until the internal temperature reaches 165°F and the chicken is cooked through.
Remove the chicken from the heat and let it rest for 5 minutes before slicing.
Garnish with fresh cilantro and serve with your choice of sides, such as rice or steamed vegetables.