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1
Whisk oil, salt, paprika, chipotle pepper, cayenne pepper, black pepper, and garlic in a bowl to make marinade. Place chicken breasts in marinade and turn to coat evenly. Cover bowl with plastic wrap and refrigerate for at least 2 hours.
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2
Spread sugar in a saucepan set over medium heat. Do not stir, but watch closely as sugar begins to melt after about 1 minute. As 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 pan from heat. Pour in vinegar and stir until sugar dissolves.
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3
Place 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 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.
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4
Set a strainer over a bowl. Strain berries, using a spatula to push through as much juice as possible. Discard skins.
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5
Preheat an outdoor grill for medium-high heat and lightly oil the grate. Drain excess marinade from chicken.
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6
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.
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7
Serve breasts on a swirl of blueberry sauce with more sauce drizzled on top.
