Set the Instant Pot to ‘Sauté’ mode and heat the olive oil.
Add the diced onion, carrots, and celery to the pot and sauté for 4-5 minutes until the vegetables soften.
Add the minced garlic and sauté for 1 minute until fragrant.
Pour in the chicken broth and stir in the dried thyme, dried oregano, salt, and black pepper.
Place the chicken breasts into the broth, ensuring they are submerged.
Secure the Instant Pot lid and set the valve to ‘Sealing’.
Select ‘Pressure Cook’ or ‘Manual’ mode and set the timer for 10 minutes on high pressure.
When the cooking time is complete, allow a natural pressure release for 10 minutes, then carefully turn the valve to ‘Venting’ to release any remaining pressure.
Open the lid and carefully remove the chicken breasts. Shred the chicken using two forks.
Add the spiralized zucchini noodles to the pot and stir to combine.
Return the shredded chicken to the soup and stir.
Set the Instant Pot to ‘Sauté’ mode and cook for an additional 2-3 minutes until the zucchini noodles are just tender.
Turn off the Instant Pot and stir in the chopped fresh parsley.
Ladle the soup into bowls and serve hot.