The world's biggest military and a dead Bin Laden are apparently not enough to make some Americans feel secure.
If the petition gains 25,000 names then a US government official is obliged to at least consider the proposal.
The Death Star has, until now perhaps, remained a figment of the the (as far as we know) imaginary 'Star Wars' universe. It is a moon-sized laser capable of destroying an entire planet with one super-evil beam.
Earlier this year it was calculated that the Death Star would cost more than £541 trillion just for the raw materials - or 13,000 times the gross domestic product of the Earth.
However there are early signs that the petition may not be honoured.
Several names turn up multiple times, including the mysterious "Vader. D" who is listed three times and reported as living in Seattle, Burlington, North Carolina, and Canyon Country, California.