In a 10-inch frying pan over medium-high heat, brown the sausage, breaking up the meat with a fork into little pieces. Drain the grease, remove sausage to a bowl, and set aside.
Add the olive oil to the frying pan over medium heat. When oil is hot add the onion, celery, and bell pepper. Cook until vegetables are soft, but not brown, about 3 to 5 minutes.
Return the sausage to the pan, add poultry seasoning and stir to combine. Add rice and seasoning packet and cook for 5 minutes, stirring frequently. Add chicken broth and bring to a boil. Reduce heat to low. Simmer, covered tightly, for 25 minutes.