In a 6-quart slow cooker, layer the carrots, garlic, sliced onion and half of the cilantro. Sprinkle with the herbs. Top with the chicken in a single layer. Pour the Worcestershire sauce and 2 quarts water over the top, sprinkle with 1 teaspoon salt, cover and turn on high.
Your soup will be done in 4 to 6 hours, though you can hold it for longer. (My slow cooker can be programmed to switch from high to a “keep warm” temperature for up to another 6 hours. Some slow cookers click to “keep warm” automatically; others need to be switched manually.)
About an hour and a half before you want to serve dinner, add the rice, turn the slow cooker to high, cover and cook until the rice is cooked through, about an hour. Remove the chicken pieces, pull off the skin and discard, then pull the meat from the bones in coarse shreds. Keep warm, covered with foil, in a low oven or microwave to warm just before serving.
Taste the soup and season with salt if necessary (it sometimes needs about 1/2 teaspoon). One of the hallmarks of this soup is little beads of golden chicken fat floating on the broth; if that’s not to your taste, spoon them off.
Pull out and discard the cooked cilantro. Chop the remaining fresh cilantro and rinse the chopped onion under cool running water. Set them out on a serving plate with the chopped green chiles, avocado and lime.
Divide the chicken among warm bowls and ladle the soup over it. Pass the garnishes for each person at the table to add al gusto.