It's extremely difficult, especially right now in the current economy. While Yale is hiring, they also have a history of trying to squeeze out the clerical and technical worker's union. Since the economy is so bad and so people are looking for work, Yale takes advantage of this by hiring Ph.D.'s to do ordinary grunt work. This fills the position and obviates the need to hire into the union.
Also, depending on what area you want to work in, Yale HR is reporting from 3 to 30 applicants for each job vacancy. Be aware too, that most of the Yale community rolls on grants. I all but had a position there a few weeks back. But, at the last minute, funding was pulled away from the hiring supervisor who turned around and cancelled the position. It's all about money.