1 tablespoon vegetable oil
1 tablespoon kosher salt
1 tablespoon paprika
1 teaspoon ground dried chipotle pepper
1/2 teaspoon cayenne pepper
1/2 teaspoon freshly ground black pepper
2 cloves minced garlic
4 skinless, boneless chicken breast halves
1/3 cup white sugar
1/3 cup apple cider vinegar
2 cups fresh blueberries
salt and freshly ground black pepper to taste
Whisk oil, salt, paprika, chipotle pepper, cayenne pepper, black pepper, and garlic in a bowl to make the marinade. Place chicken breasts in the marinade and turn to coat evenly. Cover the bowl with plastic wrap and refrigerate for at least 2 hours.
Spread sugar in a saucepan set over medium heat. Do not stir, but watch closely as the sugar begins to melt after about 1 minute. As the sugar melts it will gradually turn a golden color. Continue watching but not stirring. When all sugar has melted and golden color just begins to darken a bit (after 1 minute or less), remove the pan from heat. Pour in vinegar and stir until sugar dissolves.
Place the pan over medium-high heat and add blueberries to the sugar-vinegar mixture. Bring to a simmer, reduce heat to medium-low, and simmer until blueberries soften and mixture begins to thicken, 4 or 5 minutes. It should be a syrup-like consistency. If the sauce seems too thin, simmer a few more minutes. If it seems too thick, add a splash of water. Stir in salt and pepper. Remove from heat.
Set a strainer over a bowl. Strain berries, using a spatula to push through as much juice as possible. Discard skins.
Preheat an outdoor grill for medium-high heat and lightly oil the grate. Drain excess marinade from chicken.
Place chicken breasts on preheated grill. Cook until no longer pink in the center and the juices run clear, about 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Transfer chicken to a plate and allow to rest a few minutes.
Serve breasts on a swirl of blueberry sauce with more sauce drizzled on top.