It’s an element of A New Hope that has bubbled along for over 40 years, whether Han Solo fired his blaster first or if Greedo made the first move. A generation of kids saw Han gun down Greedo, while later ones saw them fire together, and now the recently released The Star Wars Archives: 1999-2005 gives George Lucas the chance to have the final say, and it could be argued that it alters the arc of the character as we know it.
Succinct, but there you have it, according to Lucas Han was never a cold-blooded killer but acting in self-defence. Along with the Makers final words on the subject, Mark Hamill also had his say on the subject.
“Before this conversation gets any more political allow me to state the fact that not only did Han shoot first, Greedo did not shoot second because Han was THE ONLY ONE WHO SHOT. I shed no tears for Greedo but that’s just what went down”