Chambers was found guilty of sending a menacing message in May. He was directed to pay a 385 pounds fine, a 15 pounds victim surcharge and 600 pounds costs.
Chambers, from Doncaster, South Yorkshire, claimed that he sent the tweet to his 600 followers as he was frustrated after nearby Robin Hood Airport was closed by snow.
The Twitter message read, "Crap! Robin Hood Airport is closed. You've got a week and a bit to get your shit together, otherwise I'm blowing the airport sky high!"
Chambers' solicitor told Doncaster Crown Court the tweeter message was nothing more than "facetious parody" and that the conviction should be quashed as it couldn't be called "menacing".