Heat olive oil in a large pot over medium heat.
Add diced onion, carrots, and celery to the pot and sauté for 5-7 minutes until vegetables are softened.
Stir in minced garlic and cook for 1 minute until fragrant.
Pour in the chicken broth and bring to a boil.
Add rinsed wild rice, dried thyme, dried rosemary, salt, and black pepper to the pot.
Reduce heat to low, cover, and simmer for 40 minutes or until the wild rice is tender.
In a small bowl, whisk together Greek yogurt and all-purpose flour until smooth.
Slowly ladle about 1 cup of hot soup broth into the yogurt mixture, whisking constantly to temper it.
Gradually stir the tempered yogurt mixture back into the soup pot.
Add shredded cooked chicken to the soup and stir to combine.
Cook soup for an additional 5 minutes over low heat, stirring occasionally, until heated through and slightly thickened. Do not boil after adding yogurt.
Remove from heat and stir in chopped fresh parsley.
Serve hot.