In a medium bowl toss together chicken and Cajun seasoning. In a 5- to 6-qt. Dutch oven heat oil over medium-high. Add half of the chicken, half of the sausage, and the garlic; cook and stir until chicken is browned. Remove chicken mixture. Repeat with remaining chicken and sausage; drain off fat. Return all of the chicken mixture to pan. Add broth, salt, thyme, paprika, and pepper.