To poach the chicken: Combine the chicken, onion, celery, carrot, garlic, thyme, pepper and a tablespoon of salt large pot. Add water to cover, at least 3 quarts. Bring the water to a simmer over medium heat, skimming occasionally. Skim, add more water if necessary to keep the chicken covered, and continue to gently simmer until the chicken is fully cooked (the juices from the thigh will run clear), about 40 minutes. Drain the chicken reserving the broth. Allow the chicken to cool then remove the meat from the bones. Discard the bones and refrigerate the meat until ready to make the chowder. Measure out 1 1/2 quarts of the broth and reserve for the chowder. Freeze or refrigerate any remaining broth until needed for another purpose.

To make the chowder: Heat the bacon and olive oil in a large pot over medium heat. Cook until the bacon fat is rendered and the meat firming but not yet crisp, about 5 minutes. Add the celery and onions. Reduce the heat to medium-low and cook, stirring occasionally until the vegetables begin to soften, about 6 minutes. Add the potatoes, corn, and thyme. Continue to cook, stirring occasionally, until the onions are fully soft, about 8 additional minutes.

Add the chicken broth to the pot. Bring the broth to a simmer over medium-high heat. Turn down the heat to medium and simmer until potatoes are tender, about 10 minutes. Add the cream and reserved chicken. Return the chowder to a simmer, season to taste with salt and pepper. Ladle into warm bowls and serve.