Depot Diner has steak and eggs on their menu. I haven't had it, but if it's like everything else on the menu, it should be good (altho it will probably be a grilled diner steak rather than a prime steakhouse version):
Depot American Diner
5840 W. Roosevelt Rd
Chicago, IL 60644
(773) 261-8422
"The fork with two prongs is in use in northern Europe. In England, they’re armed with a steel trident, a fork with three prongs. In France we have a fork with four prongs; it’s the height of civilization." Eugene Briffault (1846)