There are clearly-marked vegan options on the menu but there are also some unmarked options, so be sure the ask about it. Technically they don't take reservations but if you have a large group you can call ahead, they're very accommodating. Cash only.
There are a few vegan options labeled in every category. They have a vegan mayonnaise sauce also, which comes with some of the appetizers and the vegan sushi specials.
Rotating vegan specials, vegan slices on Tuesdays and Thursdays, and made-to-order vegan pies any time. Sometimes they have sides of house-made vegan ranch available.
Vegan steak and fries pizza. Need I say more?
In addition to the many clearly-marked vegan options, there are many secretly vegan items that may not be part of the regular menu, like vegan butterscotch cookies. Ask the staff about it.
While the Chicago Diner proudly proclaims it's been "meat free since '83," Original Soul Vegetarian has been providing vegan food since 1980. Everything from their seitan ribs to perfectly tender (but never mushy) collard greens, is delicious. Hours and info on their website: