Raising Rent for inherited below market rental

[Jason Bach]

My wife and I recently purchased a 3 flat in Chicago. We have done some major remodeling to our unit (now a duplex to the basement) and also the top floor unit. When we bought we inherited a lease for the 2 bedroom, 1 bath with ample storage and an enclosed back porch. Many realtors have informed us, and I have confirmed, that $875 for a 2 bedroom in our area is far below market and almost laughable (we had no issue renting out the top unit at $850). My wife and I love the 2nd floor tenant as they are great and quite easy to get along. We are hoping to raise the rent to $975 for the current tenant when the lease expires in March (still below market and we should be able to get 1100). My question is what is the best way to go about this while still being respectful and not incurring any backlash? We are thinking of having the discussion soon to give ample time to set up a move if this were to happen. 

Probably thinking too much....

Jason