Heat oil in a Dutch oven or a large heavy pot over medium-high heat; saute onion until browned, 5 to 7 minutes. Add chicken and cook until browned, 2 to 3 minutes per side.
Mix water, tomato paste, paprika, cinnamon, turmeric, salt, pepper and saffron together in a bowl; pour over chicken. Add more water if chicken isn't completely covered in liquid. Cover Dutch oven and cook over medium-low heat until chicken falls off the bone, about 1 1/2 hours.
Carefully transfer chicken to a glass serving dish. If sauce is not the consistency of gravy, add 1 to 2 tablespoons tomato paste and simmer over medium-low until it reduces to a thick gravy, about 5 minutes. Pour sauce over chicken.