First prepare your grill. Light charcoal on one side only and wait until the coals turn gray with ash.
Cut your whole chicken in half lengthwise. Season both pieces well with salt. Place the chicken skin-side up on the cool side of your grill (the side without charcoal). Close the grill's lid and let it smoke for 15 minutes.
Turn up the heat by opening your grill vents fully. Move the chicken directly over the hot coals and grill both sides until they're nicely charred. Take the chicken off the grill and let it cool enough to handle. Once cool, cut it into smaller pieces.
Heat some oil in a large pot over medium heat. Add your celery, ginger, onions, and garlic. Cook these until the onions turn clear and everything smells fragrant, about 3-4 minutes.
Add your chopped chicken and speck (or etag if you have it) to the pot. Pour in the rice wine and add enough water to just cover the chicken. Bring everything to a boil, then lower the heat and let it simmer gently for 30 minutes.
Check that the chicken is getting tender, then add your sliced chayote. Let it cook for 8 minutes.
Add the bok choy last. Let it cook for just 2 minutes until the leaves are bright green but still crisp.
Taste the soup and add salt if needed.
Serve hot in bowls with steamed rice on the side. If you like spicy food, serve some fresh chilies on the side.
The soup will taste even better the next day after the flavors have had time to develop in the refrigerator.