This gun isn’t particularly powerful, but it is extremely rare, which makes it the perfect weapon to show off to your friends (and enemies). Up to 110 rounds can be gained as a reward for completing the quest Trip to the Stars. A random amount of rounds found on the alien in the cave near the UFO crash site, plus whatever is in the magazine.
How do I get the Alien Blaster in Fallout 1? It’s off the road to the north of the ruins of Somerville (north-east of Vault 81, south-west of the Beantown Brewery), you can discover a downed flying saucer by following the path of destruction it left through the woods.
The Alien Blaster can be found at an unmarked map location that appears to be a Crashed UFO.