A third response is for users to educate themselves on the nature of asynchronous (or semi-asynchronous) communication. A letter sent and received, doesn't immediately receive a response unless wrapped in a synchronous mode (like a telephone call to inform the sender of receipt followed by reading the letter and responding).

Chat is between letters and telephones.

Chat msg are delivered whether I am ready or not. Telephone calls are received only when I am able to. Letters are delivered whether I am there to receive them or not.

Reading a chat msg is immediately communicated (along with the status of being online) though a response is a manual activity and decision. Responding to a phone msg. happens synchronously (or is treated as an awkward pause). Reading a letter is not communicated immediately though the response is a manual activity and decision.

Given this in-between nature, it might help for users to be familiar that chat msg. can be delivered and "read" but one must wait for the letter to be written by the other and sent when deemed fit.