This is a unique weapon. It can be obtained from the body of a dead alien lying a few feet away from his crashed spaceship. The alien crash site is found north of MDPL-13 Power Station and northwest of the Greener Pastures Disposal Site. It has unique ammo as well, the Alien Power Cell, which is exceedingly rare. The chance of a critical strike with this gun is nearly 100%. It can be repaired with the Firelance, but degrades incredibly quickly. Its damage is 100.
Use the following trick if you have bad karma and need more ammunition for the Alien Blaster. Go to Fort Independence. If you have a lockpicking skill of 100, use the lower levels entrance. If not, use the main entrance. Go to the lower levels and kill all the outcasts. Enter the room where an outcast was observing a computer. Go to the door on your left (lockpick skill of 75 required) and get all the ammunition in the containers. The second table with ammo boxes should have Alien Blaster ammunition. You should get a total of 18 to 24 rounds.