In a large glass bowl, combine lime zest and juice, ginger, garlic, sugar, cumin, curry powder, and soy sauce. Slowly whisk in coconut milk until mixture is smooth. Submerge chicken breast halves in marinade, making sure the marinade gets under the skin; cover, and refrigerate for at least 4 and up to 12 hours.
Preheat oven to 475 degrees. Cover a rimmed baking sheet with foil and fit with a wire rack. Remove chicken from marinade and shake to remove excess. Arrange in a single layer on rack, skin side up. Roast until an instant-read thermometer registers 165 degrees, 30 to 35 minutes.
While chicken is cooking, pour leftover marinade into a small sauce pan. Bring to a boil; reduce to a simmer and cook until sauce has reduced a little and thickened.