In small bowl, whisk together peanut butter, rice vinegar, honey, chili sauce, lime zest, salt, ginger, and 1 Tbsp water until smooth. If needed, add more water, 1 tsp at a time, until pourable consistency is reached. Taste and add more chili sauce if desired.
Preheat grill to medium. Season chicken thighs lightly with salt and pepper. Place on greased grill and close lid. Cook thighs on each side for 5 minutes, or until cooked through (internal temperature taken with instant-read thermometer should reach 165 F).
Alternatively, grill chicken in grill pan on stovetop. Slice chicken when cool enough to handle.
Divide salad greens, mint, carrots, chicken, and raspberries among serving plates. Drizzle peanut butter dressing over top and garnish with granola.