Add the chicken pieces, vinegar, water, garlic, and ginger to a pot; add a bay leaf. Season with salt and pepper and bring the whole affair to a boil over high heat.
Reduce the heat, cover the pot, and let it simmer for half an hour until the chicken becomes tender. Set the pot aside.
Heat some vegetable oil in a skillet and add the boiled chicken pieces, sauté until they get a beautiful brown color. Remove excess fat from the skillet and add the reserved sauce to the skillet.
Simmer uncovered until the water is reduced to half, and a thicker sauce is starting to form.
Add the coconut milk and continue to cook for a couple of minutes. Your coconut milk adobo chicken is ready to be served.