Place the potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two. Place the potatoes into the refrigerator to cool. When the potatoes are cool, grate them into a large bowl.While the potatoes are boiling, place the eggs into a saucepan in a single layer and fill with water to cover the eggs by 1 inch. Cover the saucepan and bring the water to a boil over high heat. Once the water is boiling, remove from the heat and let the eggs stand in the hot water for 15 minutes. Pour out the hot water, then cool the eggs under cold running water in the sink. Peel once cold.Dice the cooked eggs and dill pickles. Place the eggs and 2/3 of the dill pickles into the salad bowl with the potatoes; reserve the rest of the pickles. Place 3/4 of the peas into the bowl, and reserve the rest. Place the chicken breast meat into the bowl. Add 1/2 cup of mayonnaise and black pepper, and very lightly stir the mixture together so that the ingredients are well coated, but the peas stay whole. Place the salad in an attractive mound on a platter, and spread 1/2 cup of mayonnaise over the salad in a layer. Arrange tomato slices over the salad, and decorate with reserved diced pickle and peas.