Tenant wants to leave because of noisy neighbor

[Sagar Joshi]

I am currently renting my 1 bd 1 ba apartment in downtown Chicago. I have a very noisy (mentally sick) neighbor living in the unit downstairs. He's a miserable lad who used to be a wife beater and we called cops on him when I used to live there. The cops arrested him and the noise stopped for a while. However, now it has started again for the past few months and my tenant is being woken up in the middle of the night due to this guys yelling. For this reason my tenant wants to leave early and break the lease. 

Additionally, the building knows about this. They have tried to talk to this noisy person but due to his mental condition there is not much anyone is able to do about it. Last time I reached out to the building, they told me to call the cops on him.

I am moving out of state next month for a new job and my concern is I am going to have to deal with this every time a tenant moves in as this is directly impacting my ability to rent the unit.  I am not talking to this person directly because from my past experience (when I had to call cops on him) he seems to be a violent person and I am concerned for my safety.

What are my options to deal with this situation? Should I seek legal advise and take this person to court?