Rick there are two ways to do this. Leaving from Paris you can take the small van tours by Parisvision tours.. they have big bus tours, ,but they also offer the smaller van tours. Expensive but for many worth it. I did the big bus tour about 10 years ago and it wasn't as bad as one might imagine. We left very early in am.. then visited three Chateau ( Cheverny, Chambord and one other forget name at moment) . We had enough time to have a quick escorted tour around the palaces.. maybe 45 minutes.. then always had another 45 minutes to 1.5 hours to explore grounds and rest of palace on our own.
Another way of doing it is to get a train from Paris to Tours.. from there you can take the Acco Dispo tours .. they are small van tours and apparently well thought of..
I have to say my first trip was 3 days and using a rental car and that is the best way to do it. but I understand one simply does not always have the time.. or wish to self drive and the tours are a viable option.