Meatballs: In bowl, combine chicken, bread crumbs, green onions, garlic, ginger and soy sauce. Firmly roll by 2 tbsp into balls; arrange on rimmed baking sheet. Refrigerate for 10 minutes.
In large nonstick skillet, heat oil over medium heat; cook meatballs, stirring occasionally, until browned, about 4 minutes.
Broth: Meanwhile, in saucepan, heat oil over medium-high heat; sauté bok choy, carrots and half of the green onions until slightly softened, about 3 minutes. Add ginger, garlic and half of the chili pepper; sauté for 1 minute.
Stir in meatballs, broth and 1 cup water; bring to boil. Reduce heat to simmer, cover and cook until instant-read thermometer inserted in several meatballs reads 165°F, about 5 minutes. Discard ginger. Stir in lime juice, soy sauce and salt.
Divide meatballs among serving bowls; top with broth mixture. Sprinkle with remaining chili pepper and green onions.