In a large pot set over medium-high heat, cook the diced bacon until browned.
Add the diced onion and sliced celery, stirring occasionally until the onion begins to turn golden. Add the garlic, salt, thyme, and pepper, cooking for an additional minute.
Pour in the chicken broth, using a spoon to scrape up any browned bits from the bottom of the pot.
Add the potatoes, corn, and whole chicken breasts, ensuring the chicken is fully submerged in the broth. Bring to a gentle simmer, then reduce heat to medium.
Cover the pot and cook for 15-20 minutes, or until the potatoes are tender and the chicken is fully cooked. Lower the heat to low.
Remove the chicken breasts from the pot, shred them, and return the shredded chicken to the soup.
In a small bowl, whisk together the cream and corn starch, then gradually add this mixture to the pot, stirring until the soup thickens slightly.
Serve hot, garnishing with shredded cheese, green onions, and crumbled bacon as desired.