Cut the quarter of winter melon into approximately 2 x 1.5" big rectangles. Be sure to cut the rind of the melon off.
Peel the ginger and cut 4-5 slices, each piece ~1/8" - 1/4" thick.
Rinse the enoki mushrooms. Cut the bottoms off (if they are still connected together) and peel tiny clumps of enoki apart (as big or as small clumps as you want).
Put winter melon, enoki mushrooms, and ginger in a soup pot. Add 3 cups of water + the carton of chicken stock. Have the soup come to a boil, then add the chicken. Since it's easy to overcook chicken, let the soup cook the winter melon and mushrooms first, then put the chicken in afterwards and wait for that to cook.
After chicken is cooked, add salt (if desired).
Voila! Simple winter melon soup with chicken! :)