Combine stock, water, ginger, garlic, soy and chilli in a saucepan; cover and bring to the boil.
Add chicken to the pan; cover and simmer for 10 minutes or until chicken is just cooked. Remove chicken from stock.
Trim stalks of bok choy and separate leaves. Return stock to the boil and stir in bok choy leaves, noodles and capsicum; cook until vegetables are just tender.
Cut chicken breasts across the grain in thick slices. Divide noodles and broth into serving bowls, top with chicken, green onions and coriander.