Soften the vegetables. Heat the olive oil in a large Dutch oven or heavy cooking pot over medium-high. When the oil shimmers, add the onion, celery, carrots, and garlic. Season with a good pinch of salt and pepper. Cook, tossing occasionally, until the veggies have softened, about 5 minutes.
Poach the chicken. Add the chicken, chicken stock, and water. Season with the oregano, turmeric, red pepper flakes, and another dash of salt and pepper. Bring to a boil, then turn the heat to medium-low. Cook until the chicken is nearly fully cooked, 10 to 15 minutes. Spoon out any foam that bubbles to the top of the cooking liquid.
Cook the orzo. Transfer the chicken to a rimmed plate for now. To the pot, add the orzo and peas. Raise the heat to bring the liquid to a boil.
Shred the chicken. Using two forks, shred the chicken breasts into smaller pieces. Add the shredded chicken to the pot and cook until the orzo is tender (al dente), about 8 minutes longer.
Finish and serve. Turn the heat off and stir in the lemon juice and zest, green onion, and fresh parsley. Enjoy!