In a large pot over medium heat, heat oil. Add onion and jalapeño and cook, stirring, until softened, about 8 minutes. Add garlic, oregano, and cumin and cook, stirring, until fragrant, about 1 minute. Add chicken, broth, and chiles; season with salt and pepper. Bring to a boil, then reduce heat and simmer, uncovered, until chicken is tender and cooked through, 10 to 12 minutes. Transfer chicken to a plate and shred with 2 forks.
Add beans to pot and bring to a simmer. Cook, smashing about one-quarter of beans with a wooden spoon, until slightly thickened, about 10 minutes. Add corn and shredded chicken and cook, stirring, until heated through, about 1 minute more. Remove from heat and stir in sour cream.
Ladle chili into bowls. Top with avocado, cilantro, chips, and cheese.