Place an egg in a saucepan and fill with water to one inch above the egg. Bring the water to a rapid boil over high heat. Once boiling, cover the pot with a lid and remove the pot from the heat. Do not lift the lid. Set a timer for the type of boiled egg you want, about 4-12 minutes (longer is more hard-boiled).
While waiting for the egg to cook, cut the chicken breast into small cubes.
Preheat a frying pan. Add one tablespoon olive oil and chicken cubes. At medium heat, saute until chicken is cooked to your likeness, about 7-10 minutes. Stir occasionally.
When the egg timer goes off, drain the hot water and fill with cold water. Leave the egg in cold water for 3 minutes, then remove. Gently tap the egg against a hard surface and peel away the shell. Rinse the peeled egg under cold water to remove any bits of shell and pat dry. Cut the egg in pieces.
In a small bowl, whisk together Greek yogurt, olive oil, lemon juice, mustard, oregano, garlic powder, salt, and pepper. Set aside.
Place chopped romaine lettuce, sliced tomato, and chopped avocado on a dinner plate. Top with sliced eggs and cooked chicken. Drizzle everything with dressing and sprinkle with Parmesan cheese.