Why does transmission slip when going in reverse up hill?

It is not normal for a trans to slip. It may be a common problem but not normal. My recommendation would be to take it to a reputable repair facility and have it diagnosed. Our shop is in Delavan and we do have a Chrysler Certified Tech on staff. We are about 40 minutes from Woodstock. Feel free to give us a call 262-728-2944. Hope to hear from you.