1) Preheat the oven to 350° F.
2) Thinly slice and place the potatoes in a cold water bowl, drain well and dry over a paper towel.
2) In a large heavy skillet or a flameproof casserole, heat the oil for 1-2 minutes over a medium-low heat.
3) Spread and slightly press down the potato slices, then saute without stirring until crisp and cooked.
4) Sprinkle the potatoes with the salt, pepper, chives, and cheese.
5) Individually crack the eggs in a cup and gently slide them over the cheese.
6) Bake without the lid for about 5-8 minutes until the eggs are cooked as desired.
7) Slice into portions and serve in nice plates.