Heat olive oil in a large pot over medium heat.
Add diced onions, carrots, and celery. Cook until softened, about 5-7 minutes.
Stir in minced garlic and cook for 1 minute more.
Add diced chicken breast, cooking until no longer pink.
Pour in chicken broth and bring to a boil.
Add wild rice and thyme, reduce heat to low.
Cover and simmer for 30 minutes, until rice is tender.
Season with salt and pepper to taste.
If desired, stir in some chopped parsley for freshness.
Serve hot, garnished with additional herbs if you like.