Set the Instant Pot to ‘Sauté’ mode and heat the olive oil.
Add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic, sliced carrots, and sliced celery. Cook for another 2 minutes, stirring occasionally.
Stir in the dried thyme, dried oregano, salt, and black pepper.
Pour in the chicken broth and add the whole chicken breasts to the pot.
Close the Instant Pot lid and set the valve to ‘Sealing’.
Select ‘Pressure Cook’ or ‘Manual’ mode and set the timer for 10 minutes.
When the cooking time is complete, allow the pressure to release naturally for 10 minutes, then carefully perform a quick release to release any remaining pressure.
Open the lid and remove the chicken breasts. Use two forks to shred the chicken into bite-sized pieces.
Return the shredded chicken to the pot.
Add the spiralized zucchini noodles and stir to combine.
Set the Instant Pot to ‘Sauté’ mode and cook for 2-3 minutes until the zucchini noodles are just tender.
Turn off the Instant Pot and stir in the chopped fresh parsley.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot.