1. Prepare the ingredients by washing the chicken pieces, slicing the ginger, chopping the onions, mincing the garlic, peeling and cutting the green papaya or chayote, and rinsing the leafy greens.
2. Heat cooking oil in a large pot or deep pan over medium heat.
3. Sauté the ginger, garlic, and onion until fragrant and the onions are translucent.
4. Add the chicken pieces to the pot and cook for about 5-6 minutes until lightly browned.
5. Pour in the fish sauce, stirring to coat the chicken evenly while releasing its aroma.
6. Add the chicken stock or water to the pot, ensuring the liquid fully covers the chicken.
7. Bring to a boil, then reduce the heat to low and let the soup simmer for 25-30 minutes. Skim off any foam or impurities that rise to the top.
8. Add the green papaya or chayote wedges to the pot and simmer for another 10-12 minutes until they are fork-tender.
9. Season the broth by tasting and adjusting with salt or additional fish sauce if necessary.
10. Stir in the leafy greens (such as malunggay, chili leaves, or spinach) in the final 2-3 minutes of cooking. Allow them to wilt slightly while maintaining their vibrant color.
11. Serve the Chicken Tinola hot, paired with steamed rice and a side of fish sauce with calamansi for dipping, if desired.