To Brine the Chicken: Fill a large container with 4 quarts water. Pour the salt and sugar into the water and stir until dissolved. Put the chicken breasts in the brine, cover, and refrigerate for 1 1/2–2 hours.
In the meantime, make the relish and the glaze.
To Make the Relish: In a medium bowl, combine the lime juice, olive oil, chili powder, chopped orange, green onions and mint until the pieces of orange are evenly coated with juice, oil and seasonings. Cover and refrigerate.
To Make the Glaze: Combine the marmalade, soy sauce, sesame oil, vinegar and sriracha sauce to a rolling boil and continue to cook on high heat for 3 minutes. Remove from the heat and cool before using to baste the chicken.
To Finish the Dish: Preheat the grill (or a grill pan) to medium-high. Remove the chicken from the brine and dry with a paper towel. Season with the salt and pepper; then grill until an instant-read thermometer inserted into the thickest part of each reads 165°F, 5-7 minutes per side. Brush with the glaze 5 minutes before the chicken is done. Glaze again on other side about a minute before removing from the grill. To serve, top each grilled breast with one-quarter of the relish.