Heat a large Dutch oven or heavy-bottom pot over medium-high heat. Add ½ tablespoon olive oil and 1½ cups frozen corn. Spread the corn into an even layer and cook without stirring for 2–3 minutes until charred. Stir and cook another 2–3 minutes until lightly browned. Remove corn to a bowl and set aside, leaving browned bits in the pot.
Reduce heat to medium. Add the remaining ½ tablespoon olive oil, diced onion, and jalapeño. Cook for 4–5 minutes until softened. Stir in garlic and cook for 30 seconds until fragrant.
Add ground chicken and cook, breaking it apart as it cooks, until fully browned, about 5–7 minutes.
Stir in chili powder, smoked paprika, cumin, and salt. Cook for 1 minute to toast the spices.
Pour in chicken broth and the remaining 1½ cups frozen corn. Bring to a simmer and cook uncovered for 20 minutes, stirring occasionally.
For a thicker, creamier chili, blend about ¼ to ? of the chili using an immersion blender, leaving most of it chunky. This step is optional.
Reduce heat to low and stir in sour cream, lime juice, and the reserved charred corn. Simmer gently for 2–3 minutes until warmed through. Taste and adjust seasoning if needed.