Kevin's Chilly cannot be legitimately obtained as anything other than a mission item.
Being a mission weapon, it does not take up any space in a character's backpack and cannot be dropped, traded, exchanged, or placed in the player's bank.
Trivia
The flavor text is a reference to the 1984 film This Is Spinal Tap. It is also a reference to The Office episode Finale, where it is revealed that Kevin had been using the number "keleven" to balance problematic books by hometime.
The weapon name is a reference to The Office episode Casual Friday. In the episode, Kevin makes a pot of chili but drops it when bringing it to work.