Preheat the oven to 300°F.
Arrange 1 1/2 pounds boneless skinless chicken thighs in a 9-inch square baking dish in a single layer. Pat the chicken dry with paper towels if desired.
Use a sharp knife to score each thigh by making several shallow slits in the top so the sauce can penetrate.
In a medium bowl, combine the 7-ounce jar tomato paste, 2/3 cup balsamic vinegar, 3/4 teaspoon sea salt, 1/2 teaspoon black pepper, 3/4 teaspoon smoked paprika, 1 teaspoon garlic powder, 1/2 teaspoon onion powder, and 1 tablespoon brown sugar. Whisk thoroughly until the mixture is smooth and pourable.
Pour the sauce evenly over the chicken, pressing it into the slits and ensuring the thighs are well coated.
Cover the baking dish tightly with a double layer of aluminum foil.
Bake for 2 1/2 to 3 hours, until the chicken is very tender and pulls apart easily.
Remove the dish from the oven, carefully lift off the foil to avoid steam, and let the chicken rest 5 minutes.
Using two forks, shred the chicken directly in the baking dish and toss it with the sauce to coat. Serve immediately.