Rinse the wild rice under cold water and set aside.
In a large pot, heat the olive oil over medium heat. Add the onions, garlic, carrots, and celery, sautéing them until softened, about 5-7 minutes.
Add the diced chicken breast to the pot and cook until no longer pink, about 5-6 minutes.
Sprinkle in the thyme, salt, and pepper, stirring to combine.
Pour in the chicken broth and add the rinsed wild rice. Bring to a boil.
Reduce heat and simmer for 45 minutes, or until the wild rice is tender.
Stir in the heavy cream, then taste and adjust seasoning as needed.
Remove from heat and let rest for 5 minutes before serving.