Place chicken in a large pot and fill with water until chicken is covered by a 2 inches or so. Bring to a simmer on the stove, reduce heat and continue to gently simmer for about 45 minutes. Drain and set aside.
meanwhile in a large saucepan combine the remaining ingredients. Cook over medium low heat, stirring occassionally, for about 15- 20 minutes or until the blueberries are softening. Blend with an immersion blender (or you can put into the food processor) until desired consistency. Taste for seasoning.
Heat grill to medium heat. Grill chicken for about 5 minutes per side. start basting with sauce, turning every 3-4 minutes, basting 2 times per side.
Remove chicken to a serving platter and garnish with fresh chopped rosemary. Serve extra sauce on the side.
Keyword dairy-free, gluten-free, paleo, pasture-raised chicken, soups and stews