You can already do this with any normal email account. Just do myemail+whatever@domain.com. You can put anything you want behind the +, and it still works.
i.e. myemail+chase@domain.com, myemail+huffpost@domain.com, myemail+facebook@domain.com.
This used to be used as some sort of automatic labeling system that was supposed to be part of the spec eons ago, but it works just fine for generating unique emails so that you can see if/when an email has been leaked.