In a slow cooker, whisk together flour, salsa and broth until well blended. Stir in onion then arrange chicken on top.
Cover and cook on LOW for 6 hours. Remove chicken to a plate. Ladle sauce from slow cooker into a blender; puree; stir in sour cream.
Return sauce and chicken to slow cooker and keep warm until ready to serve. Arrange chicken on dinner plates and top with shredded cheese.