Combine Worcestershire, tomato paste, ketchup and 1/2 teaspoon Cajun or Creole spice mix in bowl; set aside.
Bring 3 quarts lightly salted water to boil in large saucepan over high heat. Add rice and cook, stirring occasionally, until just tender, about 12 minutes. Drain rice in fine-mesh strainer and rinse.
Heat oil in 12-inch nonstick skillet over medium-high heat until just smoking. Add chicken, andouille, bell pepper, scallion whites and remaining 1 1/2 (start with 1 teaspoon and add to taste) teaspoons Cajun or Creole spice mix and cook, stirring occasionally, until chicken is cooked through and beginning to brown, 8 to 10 minutes.
Add the cooked rice and Worcestershire mixture to skillet and cook, stirring frequently, until mixture is heated through and fully combined, about 5 minutes. Stir in scallion greens and fresh thyme, if using.