I am in the process of installing molding in our dining room. We would like to install a simple chair rail around the room with quarter round molding in each of the corners. I've seen photos (although I cannot find them now) where the quarter round molding "keys" into the chair rail very nicely. Is anyone else familiar with this? If so, how is it done?

Not sure what you mean by "keyed" but if you mean what I think you mean, the only way to do that would be to shape the end of the chair rail to match the 1/4 round. You would do that with a router and a cove bit the same radius as the 1/4 round.