Heat the vegetable oil in a large pot over medium heat. Add the ginger, onion, and garlic, and sauté until fragrant and the onion becomes translucent.
Add the chicken pieces to the pot and cook until they are lightly browned on all sides.
Pour in the water and fish sauce. Bring the mixture to a boil, then reduce the heat and let it simmer for about 25 minutes, or until the chicken is fully cooked.
Add the chayote(or papaya) wedges to the pot and continue to simmer for another 15 minutes, or until the papaya is tender.
Add the malunggay leaves (or spinach) and cook for an additional 2 minutes until the leaves are wilted. Season with salt and pepper to taste.
Ladle the soup into bowls and serve hot with steamed rice.
If green papaya is not available, chayote is a great substitute. Spinach can replace malunggay leaves if they are not accessible. For a spicier version, add a few slices of green chili peppers.