To help the chicken breasts cook more evenly, butterfly them so they are roughly the same thickness, approximately ½ inch thick. Put the chicken in a (1 gallon) freezer bag then pour one-half of the marinade in the bag. Set aside the remaining one-half of the marinade for the vegetables. Gently work the marinade throughout the bag to completely coat the chicken and seal, pressing air out. Refrigerate marinated chicken between at least 1 and up to 3 hours.
While the chicken marinates, cut up onions and peppers in ½ inch strips and add to a large bowl. Pour the reserved marinade over the vegetables and toss well to evenly coat the vegetables with the marinade. Place the vegetables in a (1 gallon) freezer bag and seal, pressing the air out. The marinade is acting as a seasoning for the vegetables at this point more than an actual marinade. Refrigerate until ready to cook.
When smoking hot, add enough chicken to form 1 layer deep. Cook the chicken about 8 – 10 minutes until golden brown on both sides and cooked through, turning every couple minutes. Chicken is done when breasts reach between150 and 160 degrees on an instant read thermometer (which I recommend and love!) When done, remove chicken to several plates to cool. Continue cooking chicken in batches until all chicken is cooked.
When all batches of the chicken are cooked, sauté the vegetables until they are mostly softened and just beginning to caramelize.
While the vegetables are cooking, slice the cooled chicken on the diagonal into roughly ¼ inch by 2 inch pieces. Add the chicken in with the vegetables and if serving immediately heat until chicken is rewarmed.
When ready to serve, Heat 1 tablespoon of oil in large skillet to smoking over medium-high heat. Add chicken and vegetables, cook, stirring until just warmed through out. Wrap flour tortillas with damp towel and microwave in 30 second increments until warm.