Place peppers, onion, tomatoes, juice, 1/2 cup chicken broth, garlic and paprika in a slow cooker.
In a large skillet, heat 1 Tbsp. oil over medium high heat. Season chicken with salt and pepper. Add to skillet and brown all sides, about 8 minutes. Transfer to slow cooker. Pour remaining 1/2 cup broth in skillet; scrape bottom of pan to incorporate browned bits. Pour liquid into slow cooker and cook on high setting for 6 hours.
Remove chicken and let cool. Remove meat from bones and return to slow cooker; discard bones. Stir in sour cream.
Cook pasta according to package directions. Toss with remaining 2 tsp. oil. Serve chicken over pasta.