In a large pot, heat the olive oil over medium heat. Add the diced chicken and cook until browned, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion, garlic, carrots, and celery. Sauté for about 5-7 minutes, until the vegetables are tender.
Return the browned chicken to the pot, and pour in the chicken broth. Stir in the dried thyme and oregano, and season with salt and pepper. Bring the mixture to a boil.
Once boiling, reduce the heat and let the soup simmer for about 20 minutes.
After simmering, add the frozen peas and heavy cream to the pot. Continue to simmer for an additional 5 minutes, allowing the flavors to meld together.
Taste and adjust seasoning if necessary. Stir in the fresh parsley before serving.
Serve hot, with optional crusty bread for dipping.