Heat the oil in a saucepan over medium heat. Add the chicken and fry until light pink in colour, then stir in the potatoes and salt. Add more oil if necessary, mix thoroughly and add just enough water to cover the chicken and potatoes. Turn down the heat to low and simmer until the potatoes are tender and chicken is cooked through.
In a small bowl, mix together the curry powder and 2 tablespoons water. Pour the curry mix into the saucepan and stir well. Add dried tangerine peel and star anise, if using. Simmer for 5 minutes more.