The alien blaster is particularly devastating as a close range weapon, and along with the turbo plasma rifle is one of the most formidable weapons in the Fallout games to date.
It can be fired for 2 action points with Fast Shot and the Bonus Rate of Fire perk. If used by a character with high skill levels and accompanying perks, it can cause up to 150 damage per hit. Very random damage and short range make it hard to consistently use effectively, requiring luck for loads of critical shots. It is also one of the most expensive guns in the game.
The alien blaster can be bought from Willy in a random encounter north of Modoc.
Additionally, the alien blaster can be picked up by hacking a terminal on the Enclave Oil rig in the maze room. By passing the Science check when using the Repair skill on a (each game randomly selected) maze room terminal one can find an Easter egg. The egg 'hatches' a special item depending on the Chosen One's tagged skill. If they have Speech tagged and over 100% the egg is the alien blaster. Note that the game checks from the ordered list (science, repair, gambling, outdoorsman, throwing, first aid, doctor, traps) first for a tagged skill over 100%, so in order to get the blaster one musn't have any of these skills tagged and over 100%.