"Stealth" interviews I am an assistant professor and was invited to do a "stealth" interview at another university. 

Should I really treat this interview as a secret (and risk that others in my department find out through the grapevine), or should I go ahead and tell my department chair now (even though it is just an interview)? What are the pros and cons of each?
There's absolutely no payoff to telling your chair that another university might be interested in you unless and until you have an offer you think you might want to accept.

If an interview visit is confidential or, as you put it, "stealth", everyone involved should know what that means and there should be very little risk that word of your visit will filter back to your home institution.