Dice vegetables & mince the garlic.
In a heavy bottom 4qt saucepan, heat vegetable oil over moderate heat.
Add vegetables and cook over medium/low heat until shiny & translucent but not browned.
Slice andouille into 1/4" pieces & cook with vegetables to render out some of the fat.
Add tomatoes & cook ~5 min over medium heat, stirring constantly. Add Cajun seasoning, chicken stock, chicken & rice. Bring to a boil, reduce heat to low & simmer for about 20-30 min until rice is tender.