Season chicken breasts with salt and pepper. Heat a large soup pot over medium-high heat. Add in 1 tablespoon olive oil. Sear chicken breasts in olive oil for 2 minutes per side until golden brown, but not cooked through. Remove from pot and set aside.
Add in remaining 1 tablespoon olive oil to the pot. Add in onion, carrots, and celery and saute 4-5 minutes. Add in garlic and toast for 1 to 2 minutes.
Return chicken to pot. Pour in chicken broth and season with thyme and oregano. Simmer for 15 minutes, until chicken is cooked through and vegetables are tender.
Use tongs to remove chicken. Shred and return to pot. Add in gnocchi and simmer for 5 minutes.
Stir in heavy cream and spinach and heat 1 to 2 minutes to wilt spinach. Season with additional salt and pepper to taste. Serve hot.