Combine flour with 1/4 teaspoon each salt and pepper. Dredge chicken pieces in flour, shaking of any excess. Reserve remaining flour.
Place 1/2 tablespoon oil in a large Dutch oven over medium heat. Brown 1/2 the chicken for 2 minutes until a little golden; turning and cooking another 2 minutes. Remove chicken to plate Repeat with remaining chicken.
Cook onions in the Dutch oven for 2 minutes. Add garlic and cook an additional minute until fragrant. Stir in the remaining flour, lemon juice, chicken broth and water. Bring liquids to a boil.
Add in the quartered potatoes, chickpeas and olives and stir. Nestle the chicken breasts bone side up into the stew. Reduce to a simmer, cover and cook for 15 minutes.
Taste the liquid and adjust salt and pepper as needed. Turn the chicken pieces and continue to cook 5 to 10 minutes until potatoes are tender and chicken is cooked through.
Stir in parsley and cook one minute.
Ladle into serving bowls.
(My nephews have asked me to note these are smaller girly portions so if you are serving teens or others with larger appetites, adjust the serving amounts accordingly).