You stumble onto a lonely man named Patrick in the desert who you can ask to sing "Na Gheala Mbeadh" if you pass a Speech check. Listening to the song increases your Charisma by one point. You can meet him again, but he will not sing the song for you anymore.
Strictly speaking this is not a special encounter. Unlike the special encounters (which can only be found on Desert squares), this encounter only happens on Mountain squares and is one of the 6 possible encounter types for north and south mountain encounters. Encountering Patrick has nothing to do with the player's Luck. Also unlike the others, this can be encountered multiple times and the resources respawn each time.
Patrick is a special encounter in Fallout. This encounter only happens on Mountain terrain squares on the world map.
Behind the scenes
'Na Gheala Mbeadh' can be translated to 'The Light Would', but it should be noted that 'Na Gheala Mbeadh' is very poor Irish.