Heat the olive oil in a large pot over medium heat.
Add the diced onion, carrots, and celery to the pot.
Cook, stirring occasionally, until the vegetables soften.
Add the minced garlic and cook briefly until fragrant.
Pour in the chicken broth and bring the soup to a gentle boil.
Add the chicken breasts whole to the pot.
Reduce the heat and simmer until the chicken is fully cooked, about 12 minutes.
Remove the chicken from the pot and shred it by hand.
Add the dry orzo pasta to the simmering broth.
Cook the orzo until just tender, stirring occasionally.
Return the shredded chicken to the pot.
Add the lemon zest, lemon juice, salt, black pepper, oregano, and red pepper flakes if using.
Stir well and taste, adjusting seasoning as needed.
Remove the pot from the heat and stir in the chopped parsley just before serving.