However, as a result of the Gunners' fourth-placed finish, Hull will play in the Europa League for the first time in their history next season.
Chester told reporters: "Seeing Arsenal lift the trophy has given me a real desire to come back here. I certainly don't want this to be a one-off. Not at all. It's been an amazing experience and I'll always remember my goal.
"But this has got to act as a springboard for us. This has been a great journey, which we've all enjoyed, but it must not be the end."
Hull finished 16th in the Premier League in their first season back in the top flight for four years.