Saute the chicken pieces in a dutch oven with 2 tablespoons oil for 5 minutes on medium high heat. Rotate the chicken to lightly brown both sides.
Add water, cover and reduce heat to low and simmer for 30 minutes.
In a large frying pan, saute the onions with the remainder 2 tablespoon oil for 10 minutes until lightly brown.
While the chicken and onions are cooking, in a food processor pulse the walnuts until finely ground. Don’t overdo it, otherwise, you will have walnut butter. Set aside.
Add the ground walnuts to the pan with onions and stir over medium heat for a couple of minutes.
Add the walnuts, pomegranate molasses, salt and pepper to the chicken. Gently stir to incorporate all the items into the pan.
Cover, keep the flame on low and continue to cook for 75 minutes. Take extra care and stir occasionally to prevent this thick stew from burning on the bottom.
The stew should have turned into a deep maroon color and the chicken should be fork tender.
Add the saffron water, stir and taste for sweet and sour levels. Adjust by adding more sugar or lemon juice.
Remove from the heat and allow to sit for 5 minutes before serving.
Serve with steamed Persian saffron basmati rice.