For red pepper sauce, place sweet peppers in a steamer basket in a large skillet or 4-quart Dutch oven. Add water to skillet to just below the basket. Bring to boiling. Steam, covered, over medium heat about 18 minutes or until peppers are tender. Transfer peppers to a blender or food processor. Add oil, salt, and hot pepper sauce. Cover and blend or process until smooth.
Sprinkle chicken with Cajun seasoning. Place chicken in the steamer basket, overlapping thinner portions as needed. Steam, covered, for 15 to 20 minutes or until chicken is done (165 degrees F).
Meanwhile, in a large saucepan cook linguine according to package directions, adding green beans for the last 8 minutes of cooking; drain. Return linguine mixture to hot saucepan. Cut cooked chicken into bite-size pieces. Add chicken and red pepper sauce to linguine mixture; toss gently to coat. Sprinkle with parsley before serving.