Whisk olive oil, herbes de Provence, garlic, salt, and black pepper in a bowl; place chicken in marinade and stir to coat. Cover and refrigerate 1 to 6 hours, turning chicken occasionally in marinade.
Whisk chicken broth, orange juice, sugar, orange zest, butter, tamarind paste, and ginger in a saucepan and place over medium-high heat. Cook at a vigorous boil, whisking often, until mixture has reduced to about 3/4 cup and glaze coats the back of a spoon, 25 to 30 minutes. Remove from heat and stir in chile-garlic sauce; season tamarind glaze with salt and black pepper.
Preheat the grill for medium-high heat. Spray a grill pan with cooking spray. Pour about 3 tablespoons tamarind glaze into a small bowl for basting and set aside.
Place chicken breasts onto preheated grill; discard used marinade. Grill chicken until browned, the meat is no longer pink inside, and the juices run clear, about 4 minutes per side, basting with reserved tamarind glaze. An instant-read meat thermometer inserted into the thickest part of a breast should read at least 160 degrees F (70 degrees C). Transfer chicken to a serving plate and serve with remaining tamarind glaze poured on top.