In a medium stockpot, heat the 2 tablespoons olive oil over medium heat, add the onions and cook until translucent, about 3 minutes. Add the ground walnuts and water and cook, simmering for 25 to 30 minutes.
Add the pomegranate sauce, 1 teaspoon salt, and 1/2 teaspoon pepper to the pot and continue to cook. When the mixture turns brown in color, add the sugar and continue to cook for 1 hour.
Place the boiled chicken in a serving bowl and top with the stew to serve.