Fry bacon in a large skillet over medium-high heat until crisp. Remove bacon with a slotted spoon and set aside to use later as a garnish. Reserve bacon drippings in the skillet.
Season chicken with salt and pepper on both sides.
Add chicken breasts to the bacon drippings in the skillet and cook over medium-high heat, just until browned on both sides (about 3 minutes per side). The chicken does not need to be completely cooked through – it just needs to be browned on each side for flavor, since it will continue cooking in the slow cooker.
Meanwhile, place onions, corn, celery, carrots, potato, and thyme in a slow cooker. Add browned chicken to the slow cooker. Pour chicken broth over top, cover, and cook on HIGH for 2-3 hours or on LOW for 4-6 hours.
Remove chicken from slow cooker and place on a cutting board.
Using a handheld stick blender, puree about half of the soup in the slow cooker. If you don’t have a stick blender, you can carefully transfer about half of the soup to a regular blender or food processor and blend until it reaches desired consistency. You might have to do this in batches, depending on how large your blender is.
Once the soup is pureed, chop or shred the chicken and stir the meat back into the soup in the slow cooker.
Stir in heavy cream, cream-style corn, and ¾ teaspoon salt. Continue cooking for about 5 more minutes, or until heated through. Taste and season with additional salt and pepper, if necessary.
Divide chowder among individual bowls and garnish with reserved cooked bacon and chopped fresh parsley.