Preheat oven to 450/230°C degrees F. Line a baking sheet with foil or a silicone baking mat, if desired. An oven-proof skillet or Dutch oven are also options and will allow you to bake the chicken in the marinade/sauce.
In a medium bowl, whisk together the coconut milk, lime juice, brown sugar, ginger, garlic, basil, salt, and pepper. Add chicken to marinade mixture and toss to coat. Marinate the chicken for a few minutes or up to 24 hours.
Place chicken onto the baking sheet or into whatever baking vessel you choose. Pour the marinade over the chicken, if desired.
Bake uncovered for about 30 minutes, or until chicken is done.
Notes
Use a whole chicken cut into pieces or use all drumsticks or thighs (any bone-in, skin-on chicken). For lower carb or sugar-free, use a brown sugar substitute or try omitting the sugar.