Mix, 2 tablespoons of lime juice, brown sugar, and cayenne pepper; pour into a resealable plastic bag. Add chicken breasts, coat will in the marinade, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 1 hour.
Meanwhile, make the sauce by whisking together the cream , coconut milk, and 1/4 cup of lime juice in a bowl. Add the cilantro and garlic, then season to taste with salt and pepper; set aside.
Preheat the grill on medium-high heat, and lightly oil grate. Remove the chicken from the marinade, and shake off any excess.
Cook the chicken and pineapple slices on the grill until the chicken is no longer pink in the center, and the pineapple slices are nicely marked, approximately 6 minutes. Serve the chicken breasts topped with a slice of grilled pineapple, and a dollop of the sour cream sauce.