Vernon,

A very rough estimate for your move will look something like that:

Typical weight for the items in 2 bedroom apartment is somewhere around 5500 lbs. With prices from New York to Chicago ranging from $0.50 to $0.65 per lb it comes to be between $2750 and $3600, without any extras such as cost of packing materials, shuttle service, etc. (see List of possible extra charges).

You could probably get it cheaper, but that would be a bit more risky, since you will have to deal with less known movers or movers with not so good reputation (which in the end might cost you even more, directly or indirectly).