In a large saucepan, heat butter and olive oil over medium-low heat. Add the onion and garlic and stir until tender but not browned.

Add diced chicken, carrot, and celery; cook, stirring, until chicken is nearly cooked through.

Add the mushrooms and continue cooking, stirring, until mushrooms are tender. Stir in flour until blended; add chicken broth and thyme.

Bring to a simmer, stirring. Cover and reduce heat to low; cook for about 10 to 16 minutes, until vegetables are tender. Add salt and pepper to taste; stir in cream and heat through.