That's what the ice bath shock is for-- it firms the skin back up again. The skin and fat is the good stuff :)
This is one of the national dishes of Singapore, btw. There are hawker stands that have been recycling the broth for decades into a super-intense brew.
Boil a really big pot of water.
Put a chicken in it. Add a few slices of ginger and some scallions.
Keep the heat on low and poach until the chicken is cooked (about 30 mins).
Take the chicken out (if you're ambitious you can douse it in an ice bath), saving the broth.
Measure N cups of broth and N/2 cups of rice (rinse the rice until the water runs clear). Stick it in your rice cooker.
Serve chicken over the rice. The leftover broth goes in the freezer to start the broth next time. Over time it will intensify.