Trim chicken breast of any fat. Chop onion, celery and carrots into small pieces. Peel and chop potatoes into 1-inch pieces. Drain peas and corn. Mince garlic.
To the bowl of a 5-6 quart slow cooker add prepared chicken and vegetables, along with salt, pepper, thyme, bay leaf and chicken broth. Cover and allow to cook on high for 4 hours.
Remove and discard bay leaf. Remove chicken breast, shred and return to slow cooker.
In a medium bowl whisk together flour and heavy cream until smooth. Pour into slow cooker, stirring to combine. Replace cover and continue cooking for an additional 30-45 minutes.
Serve warm.
