One day before serving, make 3 deep slashes across the width of each chicken breast and put into a 9-by-13-inch baking dish.
Put the curry paste into a bowl and add about 1/4 cup coconut milk.
Combine with a fork until smooth, then add remaining milk and 1/4 teaspoon salt, mixing well.
Pour over chicken, cover and refrigerate 8 to 24 hours.

Preheat oven to 475 degrees.
Remove chicken from marinade, reserving marinade separately.
Place chicken on a rimmed baking sheet and sprinkle with remaining 1/4 teaspoon salt.
Bake 25 minutes, or until just cooked through.
Meanwhile, in a small saucepan, bring reserved marinade to a boil.
Reduce heat slightly and cook at a low boil at least 1 minute, then reduce heat and simmer 4 minutes.
(Add a tablespoon of water if sauce becomes too thick.)
Stir in lime juice.
Transfer chicken to plates and spoon sauce over the top.
Sprinkle with basil if using and serve.