Add the butter and oil to a heavy bottomed pan and let melt. Add the onion, celery, and bell pepper; cook, stirring occasionally, until slightly softened, about 4 minutes. Stir in the garlic; cook 30 seconds more. Sprinkle the flour over the vegetables; cook, stirring constantly, 1 minute. Gradually stir in the chicken broth.
Add the potatoes, salt, and pepper, and bring to a simmer. Cook until the potatoes can be easily pierced with a fork, about 10 minutes.
Add the corn kernels, chicken, and cream; return to a simmer, and cook until slightly thickened, 10 to 15 minutes more.
