To take benefit of these prices you will need to prove you are a leisure traveller, on the way to luton airport, so you will need to provide either yr flight numbers or yr holiday booking reference. I don't think you will need to give this when you arrive at chester station but you may be asked to give them on your journey from chester station to the airport.
Going to luton airport by train is great, you can sleep, read (even at night), play a game, or just gaze out of the window... The other caveat to buying these cheap train tickets from the station to the airport is that there must be at least two adults travelling together. But another great advantage is that children go free. All children under 5 go free, and then one kidover five but under sixteen per adult travelling by train to the airport.
be sure to leave enough time to get to the airport early enough to eat, shop and so on, so check the times of trains from the station before you go. If you have time to kill at the airport you can always read a book or play a game again! As you have bought your train ticket in advance, you don't need to fret about the opening hours of chester station.
Or maybe you meant