Heat Dutch oven on medium-high. Add olive oil.
Add bacon bits and cook till crispy-ish. Remove to a paper-towel lined bowl. You'll add them back later. Also remove some of the bacon fat. Leave a good tablespoon behind for the next step.
Add chicken, onion, carrot, and celery to pot and cook for about 10 minutes, stirring well a few times along the way. Add salt and pepper.
Add potatoes, corn, and stock. If you're not covering the veggies, add a bit of water.
Bring to a boil, then lower heat to medium and simmer for 20 minutes. Don't cover the pot.
Now for the thickening. Here are two methods to pick from: 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.