In a large bowl or resealable bag combine soy sauce, honey, balsamic vinegar, lime juice, chilis, ginger, garlic, and mint. Add chicken and marinate for at least 30 minutes or up to 1 day.
Preheat oven to 400 degrees F. Remove chicken from marinade and place on a parchment-lined sheet tray. Sprinkle both sides of the chicken with salt and roast for about 20 minutes or until the internal temperature reaches 165 degrees F.
While chicken is cooking, separate the chard stems and leaves. Finely chop the stems and roughly chop the leaves. In a skillet, heat 1 tablespoon olive oil over medium heat and sauté stems until tender. Add leaves and rice wine vinegar and cook until they begin to wilt. Season with salt, remove from heat, and toss with scallions.
To serve, divide chard and rice into bowls, top with chicken.