In a large saucepan, combine the chicken broth, tomatoes with juice, garlic, carrot, and ginger over medium heat and bring to a boil. Reduce the heat and simmer for 10 minutes.
Stir in chicken, orange and lime juice, Tabasco (beginning with 1/8th tsp and adding more to taste).
Cover and simmer for 30 mins.
Add cooked rice just before serving. Salt to taste.