Heat the oil in a large saucepan over medium heat. Add onion, and cook for a few minutes, then add the garlic, and saute for 1 more minutes. Add the carrots, rice, chicken broth, water and salt to the pan. Bring to a boil, then reduce heat and simmer, loosely covered for about 20 minutes, or until the carrots are tender. Stir in the green chilies and lime juice. Set aside to cool slightly.
Puree the soup in small batches, in a blender or food processor. The best way to puree this soup is to place half of the solids into the food processor and add just enough of the broth to liquefy the carrots and rice. Add the rest of the solids, then stir the puree back into the remaining broth. Reheat if necessary. Serve warm.
