Heat Dutch oven on medium-high. Add olive oil.
Add bacon bits and cook till crispy-ish—8-10 minutes. Remove to a paper-towel lined bowl. You'll add them back later. You may want to remove some of the bacon fat or not, leave a good tablespoon or so behind for the next step.
Add onion, carrot, and celery to pot. Add salt and pepper. Stir well and cook for about 5 minutes. Stir in chicken and cook another 5 minutes.
Stir in bay leaf and thyme.
Add stock, potatoes, and corn. Add water if needed to completely cover veggies and chicken.
Bring to a boil, then lower heat to simmer for 20 minutes, covering pot.
Now for the thickening. After further consideration, we upgraded this recipe and added two additional thickening methods. Pick the one that best suits your current diet plan or current motivation. 1) take a couple of ladle-fulls and puree them in a blender. Add back to soup. 2) Use a potato masher to mash the potatoes and corn until you're liking the thickness. These avoid adding flour or other method.
Add the cream or milk and stir. Add back the bacon bits and a tablespoon of butter. Let the whole thing simmer away for another three minutes.
Serve, garnished with fresh parsley, chives, or green onion. Grated cheddar cheese works, too.