In recent years, George Lucas has repeatedly stated that Greedo shot at Han first in the Mos Eisley cantina. He made this clear in the Special Edition of A New Hope.
This change is primarily why I hold that Special Edition up to ridicule.
Lucas’ justification is that he doesn’t want Han to be a coldblooded killer. I disagree with that characterization of Han. But, let’s put a pin in that for a moment.