Heat oil in a Dutch oven over medium-high heat. Season chicken with salt and pepper. Cook until golden brown, about 5 minutes per side. Cut into 3/4-inch pieces; set aside.
Add vegetables to pot. Cook, stirring, 5 minutes. Add sausage; cook 3 minutes. Add garlic; cook 1 minute. Stir in stock, Old Bay, tomatoes, and 1/2 cup water; bring to a boil. Add rice and chicken. Reduce heat; simmer 5 minutes. Cover; remove from heat. Let stand until rice is tender and liquid is mostly absorbed, 30 to 35 minutes. Season with salt and pepper.