Thinly slice chicken; place in Multipurpose Steamer. Stir in 1 tsp fajita seasoning; cover and microwave on high, 3−5 min.
Meanwhile, chop peppers. Thinly slice onion.
Remove cooked chicken to a large bowl. Set aside.
In steamer (don’t wash), combine peppers, onions, tomatoes, remaining 2 tsp fajita seasoning, dip mix, and salsa mix. Cover and microwave on high until peppers are soft and sauce is hot, 3 min.
Measure 1 cup sauce into bowl with chicken. Stir in 1⁄2 cup cheese.
Divide chicken mixture between tortillas. Roll up and place seam-side down in sauce in steamer. Sprinkle remaining cheese over top. Cover; microwave on high until cheese melts, 2 min.