Place bacon in small stockpot over medium-high heat. Cook, stirring occasionally, until bacon is deep golden brown and all the fat has been rendered, about 4 minutes. Remove bacon with slotted spoon, transfer to paper towel, and set aside. Discard all but 2 tablespoons of bacon fat.
Add onions, celery, thyme, and salt and pepper to taste to stockpot; cook over medium-low heat until translucent, about 8 minutes. Add stock; bring to a boil. Reduce heat to medium; simmer 15 minutes.
Add corn, potatoes, and chile; cook until potatoes are tender, 8 to 10 minutes. Remove and discard thyme. Add half-and-half, and simmer until soup is hot. Adjust seasoning with salt and pepper, and garnish with the reserved crisp bacon pieces.