"Han Shot First" is a common cry by Star Wars fans criticizing the changes George Lucas made to the Star Wars Special Edition. It refers to the famous scene in the Mos Eisley Cantina in A New Hope where, in the original version of the film, Han escapes from the bounty hunter Greedo by shooting him under the table.
The change to this scene -- Greedo shooting first -- is a focal point of the arguments about the Special Edition changes (and further changes in the DVD releases).
The scene occurs after Obi-Wan and Luke leave the Mos Eisley Cantina. Han is about to head to his ship when he is interrupted by Greedo, a reptilian alien, who asks: "Going somewhere, Solo?" Han replies that he is going to pay Jabba the Hutt, a notorious gangster, for the illegal shipment he had to dump before being boarded by Imperials. Greedo explains that it is too late, and that "every bounty hunter in the galaxy" will chase after the bounty on Han's head.
In the original version, Han nonchalantly reaches for his gun during the dialogue and, without warning, shoots Greedo under the table. He tosses the bartender a tip ("Sorry about the mess") and leaves. In the Special Edition version, Greedo fires a wild shot seconds before Han shoots him under the table. This was altered again in the DVD release, where Han and Greedo shoot at roughly the same time and Han dodges Greedo's shot.
One argument against Greedo shooting first is a practical one: how could Greedo miss at a range of less than one yard? Surely he couldn't have lasted long as a bounty hunter with aim that terrible. But there is no explanation for this miss, other than the need in the story for Han to escape unharmed. Nothing startles Greedo into missing the shot, unless he suddenly realizes that Han is reaching for his gun (and again, how would he have lasted so long as a bounty hunter if he were that easily startled?).
The other main argument for Han shooting first is that the change affects his character development. Since the Cantina scene is the viewer's first encounter with Han Solo, it is important for establishing first impressions about his character. The original scene provides a clear picture of the callousness and ingenuity that Han needs to survive as a smuggler.
When Greedo shoots first, the scene's effect becomes muddled. Han gets out of the tricky situation through sheer luck (thanks to Greedo's poor aim) rather than skill. He no longer seems anti-heroic or underhanded, but merely a noble soul acting in self-defense. As a result, the change diminishes Han's character development: his starting position as a self-centered criminal is less clear and his gradual change into a hero for the Rebellion is less drastic.
George Lucas chose to change the scene because he felt Han Solo should be less anti-heroic. In an interview for Entertainment Weekly, Lucas said, "We like to think of [Han Solo] as a murderer because that's hip -- I don't think that's a good thing for people. I mean, I don't see how you could redeem somebody who kills people in cold blood." The fan counter-argument is that if Darth Vader can be redeemed after killing millions, surely Han can be redeemed after killing one person who was pointing a gun at him.
The explanation offered by Lucas, and even the subsequent change for the DVD release, did little to placate fans who were insistent that Han shot first. However, Lucas was famous spotted wearing a "Han Shot First" T-shirt on the set of Indiana Jones and the Kingdom of the Crystal Skull, leading some fans to believe that he finally changed his mind.