Season chicken with salt and pepper; coat with flour. Heat oil in a large non-stick frying pan over medium heat. Add the chicken and cook until browned, 3 minutes each side. Transfer to a plate.
Add spring onion, coriander and ¼ cup juice mixture to the frying pan, scraping up any browned bits from the bottom of the pan. Cook 30 seconds. Add the remaining juice mixture, the carrot and chicken. Bring to the boil. Tightly cover frying pan, lower heat and simmer until chicken is cooked through and carrot is tender, about 20 minutes.
Place a chicken breast on each of 4 plates. Spoon carrot mixture and sauce over the top. Garnish with parsley.