Most apartment buildings don't rent to young people with no rental history or at least those are all the ones that I've seen so far. What are ways to get approved with no rental history?Yes, you can rent an apartment with no rental history. But you're going to have to provide the paperwork that proves you can afford it. Apply for Chicago, IL apartments for rent. Apartments range from studios to 1-3 bedroom apartments for rent. If you have untraditional rental history such as living with family explain this on your application. Many applicants, especially those who've never owned a home, have a high credit score because they have no rental history. No, we do not require that you apply before you tour. Our rentals tend to lease quickly.