In a large pot or Dutch oven, heat olive oil over medium heat. Add the diced chicken and cook until browned (about 5-7 minutes). Remove the chicken and set aside.
In the same pot, add the onion and garlic. Sauté until the onion is translucent, about 3-4 minutes.
Add the sliced mushrooms, carrots, and celery to the pot. Cook for an additional 5-7 minutes until the vegetables begin to soften.
Stir in the wild rice, chicken broth, thyme, salt, and pepper. Bring the mixture to a boil.
Reduce heat to low, cover, and let simmer for 25-30 minutes, or until the wild rice is tender.
Once the rice is cooked, return the browned chicken to the pot. Stir in the heavy cream and simmer for an additional 5-10 minutes until heated through.
Taste and adjust seasoning if necessary. Garnish with fresh parsley before serving.