1. Put the potatoes in a medium saucepan with salted water to cover and bring to a boil. Reduce the heat and cook at a gentle boil until tender, about 25 minutes. Drain the potatoes.
2. When they are cool enough to handle, peel the potatoes and cut into 1/4-inch slices.
3. Meanwhile, in a small glass or stainless-steel bowl, whisk together the lemon juice, cumin, paprika, 3/4 teaspoon of the salt, 1/4 teaspoon pepper, the ginger, and the oregano. Whisk in 6 tablespoons of the oil.
4. Heat a grill pan or a heavy frying pan over moderate heat. For the grill pan, coat the chicken with the remaining 1 tablespoon oil; sprinkle with the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Cook the chicken for 5 minutes.
5. Turn and cook until browned and just done, about 4 minutes longer.
6. Remove, and when cool enough to handle, cut the chicken into 1/4-inch slices. For the frying pan, heat the oil in the pan and then season, cook, and slice the chicken in the same way.
7. In a large bowl, combine the warm potatoes with half of the dressing. Add the chicken, onion, olives, parsley, and the remaining dressing and toss.

Serves 4.