My daughter is now 23 and in her senior year at a large university. When she was 20 she purchased an old farmhouse with a barn and 3/4 acres just on the outskirts of town and has had her chickens for the last 3 years. Even though you might not purchase, you can easily rent housing with roommate(s) and have your chickens.
Just understand that they take a commitment that most young people are not willing to take on when they also have school work, possibly and job plus a social life. The question is...do you love them enough to make that commitment?
My daughter was deployed to Iraq for a year but fortunately she had asked her grandmother to come live with her when she first bought the house, so her Granny Donna took care of the birds the whole time she was gone...and did a great job! I went out a couple times a week and cleaned coops, etc, but the day to day feeding watering, letting them out and getting them in was on her.
It can be done...the question is really how much you really want it.