In a medium bowl, season chicken with Old Bay. In another bowl, season shrimp with Old Bay as well.
Cook rice according to package instructions. I recommend rinsing your rice until the water runs clear from it. This will remove the surface starch, and prevent your rice from being sticky.
In a large skillet, heat oil over medium-high heat. Cook sausage on both sides until browned, approximately 1-2 minutes on each side. Remove and add chicken. Cook chicken on both sides until browned and cooked thoroughly, approximately 7 minutes total. Remove and add shrimp. Cook for 2 minutes on each side. Remove and set aside.
In same skillet, add butter. Once butter has started to melt, add onion, bell pepper and celery. Sauté veggies until they are translucent. Add garlic, and cook additional 3 minutes, stirring to ensure you don't burn the garlic. Stir in tomato paste, and stir until paste is fully mixed with vegetables.
Stir in Old Bay, dried thyme and cayenne pepper. Whisk in chicken broth. Add bay leaves and reduce to heat to medium-low. Cover and simmer for 25 minutes, stirring occasionally.
Remove bay leaves, turn off heat and taste sauce. Season with salt and pepper, if needed. I find myself only needing a small pinch sometimes, but often it doesn't need any.
Stir in rice and cooked meats. Serve warm and enjoy.