Death Penalty

Death Penalty is a firearm. It has a 1% chance of inflicting Instant Death on a target, slaying it with a single shot.

Source
Death Penalty is dropped by Melusine (100% drop rate). It can also be found as a collectable in the Balouve Mines maze during Chapter 15. It can be sold to shops for 10,000 gil.

Trivia

 * There are several guns named Death Penalty that appear throughout the Final Fantasy series. It is usually among the most powerful guns available.
 * Melusine was added in patch 1.13, making the Death Penalty available as early as Chapter 8. However, as a level 99 boss, she can be daunting to fight if confronted while under-leveled.