You want to find the random encounter titled "UFO" which, when you enter, has a single point of interest, an energy weapon directly underneath, you guessed it, a UFO. Simply attempt to take the weapon, you will get abducted, a mini cutscene will play out where you are experimented on, and you will be back in control, only now with a unique perk stating that you were snatched up.
Unlike the beggar random encounter, which is located in the Woodlands and also has an achievement tied to it, THIS encounter will begin a mini quest line that parodies/pokes fun at the X files, where you attempt to figure out why you were taken.
If you are having a hard time finding it, I would accept a few missions as well as some tasks from Ace, who spawns fast missions with a small silver reward, and run between location to location (not entering, just running between) until you get it to trigger. It was rather fast for me but your mileage may vary.
Good luck, and as always
Happy hunting (>*_*)>
