Heat 2 tbsp oil and butter in large skillet. Cut up red potatoes into small squares and add to oil and butter. Cook on medium-high for about 20 minutes, keeping it covered and stirring occasionally. Allow potatoes to brown before really stirring up. (Watch for grease pops! ouch! )
In a separate skillet, heat on medium-high: remaining oil, balsamic vinegar, peppers, mushrooms, and beans. Stirring occasionally for 5 minutes.
Add chicken to veggie skillet and cover. Cook for 15 minutes.
If your potatoes are done ( see if the biggest ones squish easy with a fork ) then you can chow! Otherwise just put chicken veggie skillet on low & covered until potatoes are done.