1. Place chicken breast halves in a pot, cover them with water. Bring the pot to a boil, put a cover on it so the water doesn't all evaporate, and then set it to a gentle boil. Cook for about 40 minutes. (or you can bake the chicken breast halves instead).
2. In the meantime, place eggs in a pot, fill the pot with cold water to cover the eggs. Bring the water to boil, over high heat. Reduce the heat and boil the eggs for 10 minutes to get hard boiled eggs. Chill the eggs by placing them under cold running water or in a bowl of ice water.
3. Cut mushrooms into cubes.
4. Grate carrot and finely chop onion.
5. In a medium skillet, heat 1 1/2 tablespoon vegetable oil, saute onion and carrot for about 7 minutes. Remove the mixture from the skillet.
6. Add 1 1/2 tablespoon vegetable oil to the same skillet and cook mushrooms in it for about 10 minutes.
7. Finely chop the pickles.
8. Cut the cooked chicken into small cubes.
9. Finely chop the eggs.
10. Organize the ingredients into layers in the following order:
1) half of the chicken
2) thin layer of mayonnaise
5) thin layer of mayonnaise
6) carrot and onion mixture
7) the rest of the chicken
8) thin layer of mayonnaise
10) thin layer of mayonnaise
11. Let cool in refrigerator for at least 1 hour. Use a knife to cut into segments. Serve.