Chicago: Best Way To Remove Tenant From Lease

[Sam H.]

This post pertains to a property in Chicago, IL. Please provide knowledge based on this specific location! 

I have a unit with 3 tenants on the lease, but one is moving out and all 3 current tenants want her name off the lease. I don't really have an issue with this and am looking for advice on the best way to amend the existing lease to their liking. Is it best to cancel the lease and then create a new one with the 2 remaining tenants. If so, what's the best way to legally cancel the existing lease?